diff --git a/homeassistant/components/mqtt/client.py b/homeassistant/components/mqtt/client.py
index a16f7f4b9c5..9021e4fa641 100644
--- a/homeassistant/components/mqtt/client.py
+++ b/homeassistant/components/mqtt/client.py
@@ -316,7 +316,7 @@ class EnsureJobAfterCooldown:
         self._loop = asyncio.get_running_loop()
         self._timeout = timeout
         self._callback = callback_job
-        self._task: asyncio.Future | None = None
+        self._task: asyncio.Task | None = None
         self._timer: asyncio.TimerHandle | None = None
 
     def set_timeout(self, timeout: float) -> None:
@@ -331,28 +331,23 @@ class EnsureJobAfterCooldown:
             _LOGGER.error("%s", ha_error)
 
     @callback
-    def _async_task_done(self, task: asyncio.Future) -> None:
+    def _async_task_done(self, task: asyncio.Task) -> None:
         """Handle task done."""
         self._task = None
 
     @callback
-    def _async_execute(self) -> None:
+    def async_execute(self) -> asyncio.Task:
         """Execute the job."""
         if self._task:
             # Task already running,
             # so we schedule another run
             self.async_schedule()
-            return
+            return self._task
 
         self._async_cancel_timer()
         self._task = create_eager_task(self._async_job())
         self._task.add_done_callback(self._async_task_done)
-
-    async def async_fire(self) -> None:
-        """Execute the job immediately."""
-        if self._task:
-            await self._task
-        self._async_execute()
+        return self._task
 
     @callback
     def _async_cancel_timer(self) -> None:
@@ -367,7 +362,7 @@ class EnsureJobAfterCooldown:
         # We want to reschedule the timer in the future
         # every time this is called.
         self._async_cancel_timer()
-        self._timer = self._loop.call_later(self._timeout, self._async_execute)
+        self._timer = self._loop.call_later(self._timeout, self.async_execute)
 
     async def async_cleanup(self) -> None:
         """Cleanup any pending task."""
@@ -882,7 +877,7 @@ class MQTT:
         await self._discovery_cooldown()  # Wait for MQTT discovery to cool down
         # Update subscribe cooldown period to a shorter time
         # and make sure we flush the debouncer
-        await self._subscribe_debouncer.async_fire()
+        await self._subscribe_debouncer.async_execute()
         self._subscribe_debouncer.set_timeout(SUBSCRIBE_COOLDOWN)
         await self.async_publish(
             topic=birth_message.topic,
diff --git a/tests/components/mqtt/test_init.py b/tests/components/mqtt/test_init.py
index 938426d48ed..bedbf596aa7 100644
--- a/tests/components/mqtt/test_init.py
+++ b/tests/components/mqtt/test_init.py
@@ -2658,19 +2658,19 @@ async def test_subscription_done_when_birth_message_is_sent(
         mqtt_client_mock.on_connect(None, None, 0, 0)
         await hass.async_block_till_done()
         hass.bus.async_fire(EVENT_HOMEASSISTANT_STARTED)
+        await mqtt.async_subscribe(hass, "topic/test", record_calls)
         # We wait until we receive a birth message
         await asyncio.wait_for(birth.wait(), 1)
-        # Assert we already have subscribed at the client
-        # for new config payloads at the time we the birth message is received
-        assert ("homeassistant/+/+/config", 0) in help_all_subscribe_calls(
-            mqtt_client_mock
-        )
-        assert ("homeassistant/+/+/+/config", 0) in help_all_subscribe_calls(
-            mqtt_client_mock
-        )
-        mqtt_client_mock.publish.assert_called_with(
-            "homeassistant/status", "online", 0, False
-        )
+
+    # Assert we already have subscribed at the client
+    # for new config payloads at the time we the birth message is received
+    subscribe_calls = help_all_subscribe_calls(mqtt_client_mock)
+    assert ("homeassistant/+/+/config", 0) in subscribe_calls
+    assert ("homeassistant/+/+/+/config", 0) in subscribe_calls
+    mqtt_client_mock.publish.assert_called_with(
+        "homeassistant/status", "online", 0, False
+    )
+    assert ("topic/test", 0) in subscribe_calls
 
 
 @pytest.mark.parametrize(
diff --git a/tests/components/mqtt/test_mixins.py b/tests/components/mqtt/test_mixins.py
index 2bcd663c243..e46f0b56c15 100644
--- a/tests/components/mqtt/test_mixins.py
+++ b/tests/components/mqtt/test_mixins.py
@@ -335,6 +335,9 @@ async def test_default_entity_and_device_name(
 
     # Assert that no issues ware registered
     assert len(events) == 0
+    await hass.async_block_till_done()
+    # Assert that no issues ware registered
+    assert len(events) == 0
 
 
 async def test_name_attribute_is_set_or_not(