In a medium, heavy-bottomed saucepot, combine 1/2 tablespoons loose leaf Earl Grey tea and 1 cup unsalted butter. Melt the butter over medium-low heat, using a heatproof rubber spatula to swirl the butter around to ensure even melting. Once the butter is completely melted, remove from heat and allow to cool on a wire rack for 10 minutes. Place a fine-mesh sieve over the bowl of a freestanding electric mixer and strain the tea leaves from the butter, using the rubber spatula to press gently on the tea leaves to get as much butter as possible. Discard the tea leaves and allow the infused butter to cool to room temperature or closeish.
Center a rack in the oven and preheat to 350 (F). Prepare a 13 x 9-inch cake by spraying with cooking spray and lining the bottom with parchment paper. Spray the parchment paper with cooking spray as well.
In a medium bowl, whisk together 1 1/2 cups all-purpose flour, 3/4 teaspoons dried lavender, 1/4 teaspoon plus 1/8 teaspoon baking powder and 1/4 teaspoon kosher salt. Set aside.
Add 1 cup granulated sugar and 1 tablespoon light corn syrup to the freestanding electric mixer bowl containing the tea-infused butter (from the 1st step). Fit your stand mixer with a paddle attachment and cream the butter, sugar and corn syrup on medium speed until light and fluffy, about 3 to 5 minutes. Whisk together 3 eggs, 3 tablespoons sour cream, and 1 teaspoon vanilla extract in a liquid measuring cup, before pouring into the creamed butter and beating until smooth. Scrape the bottom and sides of the bowl and continue mixing until smooth.
Turn the mixer on its lowest speed and add the dry ingredients (from the 3rd step) in three batches. Mix the dry ingredients until just incorporated, before adding the next batch. Once the dry ingredients have been mixed in, scrape the bottom and sides of the bowl before mixing for another 15 seconds.
Scrape the batter onto the prepared baking sheet. It will seem like it's too thick, but spread it evenly across the pan with the offset icing spatula. Bake in the preheated oven for 25 to 30 minutes, until a skewer inserted into the center of the cake comes out clean and the cake bounces back when gently prodded with your finger. Transfer the cake to a wire rack and let cool completely before using the cookie cutters to stamp out the mini cakes and petit fours.