Add the milk, Earl Grey tea bags, and lavender to a large pot over medium-high heat. Bring the mixture to a boil, then remove from the heat and allow to cool. Meanwhile, make the cake.
Make the cake
Preheat the oven to 350°F. Line an 8-inch round cake pan with parchment paper, and set aside.
In a large mixing bowl, whisk together the flour, baking powder, baking soda, salt, ground tea leaves, ground lavender, and lemon zest.
In the bowl of a stand mixer (or in a large mixing bowl and using a hand mixer), beat the eggs until they are frothy, about 2 minutes.
Beat in the sugar, vanilla, and yogurt.
Gradually add the dry ingredients to the wet ingredients while the mixer is on low-medium speed, just until ingredients are well combined. Do not overmix.
Pour the batter into the prepared lined baking pan and bake at 350°F for 25-40 minutes, or until a toothpick inserted into the center of the cake almost comes out clean. While it's baking, clean out the stand mixer bowl and finish the buttercream.
Finish making the earl grey lavender frosting
In the stand mixer, beat the softened butter until it's light and creamy, about 3 to 5 minutes.
With the mixer on low, alternate in beating in the powdered sugar and earl grey lavender milk, until the frosting is to the thickness and consistency you desire. Add more powdered sugar if you want thicker buttercream; add a touch more milk to thin out a buttercream that became too thick.
Assemble
Once the cake is done baking, allow it to cool completely before frosting with the earl grey lavender buttercream.
Notes
Makes 15-20 servingsStorage: wrap frosted cake in plastic wrap and place in an airtight container in the refrigerator for up to 5 days.