01 - Heat the milk in a small saucepan until steaming without boiling. Add Earl Grey tea bags and 2 teaspoons lavender, steeping for 15 minutes. Remove tea bags, strain out lavender buds, and allow to cool completely. Reserve 2–3 tablespoons of the infused milk for frosting preparation; use the remaining milk for the cake batter.
02 - Preheat oven to 350°F. Grease and flour two 8-inch round cake pans. Whisk together flour, baking powder, baking soda, and salt in a medium bowl. Cream butter and sugar in a large bowl until light and fluffy, approximately 3–4 minutes. Beat in eggs one at a time, incorporating fully after each addition, then add vanilla extract. Alternately add flour mixture and infused milk to the butter mixture, beginning and ending with flour, mixing just until combined. Divide batter evenly between prepared pans. Bake for 25–30 minutes or until a toothpick inserted into the center comes out clean. Cool in pans for 10 minutes, then transfer to a wire rack to cool completely.
03 - Combine water, granulated sugar, and lavender in a small saucepan. Bring to a gentle simmer over medium heat, stirring constantly until sugar completely dissolves. Remove from heat and let steep for 10 minutes. Strain through a fine-mesh sieve to remove lavender buds and allow syrup to cool to room temperature.
04 - Beat butter on medium-high speed until creamy and smooth, approximately 2 minutes. Gradually add powdered sugar on low speed until incorporated, then increase speed to medium-high and beat for 2 minutes. Add vanilla extract and salt, mixing to combine. Beat in reserved infused milk, 1 tablespoon at a time, until desired spreading consistency is reached.
05 - Brush the tops of cooled cake layers generously with lavender syrup. Place one cake layer on a serving plate or cake stand, spread an even layer of frosting over the surface. Position the second cake layer on top, then frost the top and sides of the entire cake with remaining frosting. Garnish with additional dried lavender buds if desired.