Preheat your oven to 350°F (175°C). Grease a cake pan and set aside.
In a mixing bowl, combine the softened butter and granulated sugar. Beat with a mixer until light and fluffy, about 2-3 minutes.
Add eggs one at a time, mixing well after each addition. Stir in vanilla extract and ground lavender buds.
In a separate bowl, whisk together the flour and a pinch of salt. Gradually add the dry ingredients to the wet mixture, alternating with milk, starting and ending with the flour mixture. Mix until just combined.
Gently fold in the sliced apples, distributing them evenly throughout the batter.
Pour the batter into the prepared cake pan, smoothing the top with a spatula. Bake for 40-45 minutes, or until a toothpick inserted in the center comes out clean.
While the cake bakes, prepare the caramel glaze. Combine brown sugar, heavy cream, and butter in a saucepan over medium heat. Bring to a gentle boil, stirring constantly, until thickened slightly and caramel-colored, about 5 minutes.
Once the cake is done, remove from oven and let cool on a rack for 15 minutes. Drizzle the warm caramel evenly over the cake's surface, allowing it to set and crack slightly as it cools.
Transfer the cake to a serving plate once fully cooled and the caramel glaze has set. Slice and enjoy the moist, fragrant apple cake with its crunchy caramel top.