With tender, buttery interiors and fine, crisp exteriors, these lavender-infused tea cakes are a sophisticated treat. Our starting point was a simple butter cake, and we found that increasing the butter and replacing the milk with buttermilk gave us rich yet delicate cakes. For petite cakes that didn't dome, we baked them in a muffin tin and carefully adjusted the lavender and batter amounts. To keep the cakes from sticking and to ensure an attractive, crackly exterior, we brushed the pan with butter and sugar. After baking, we inverted the cakes so that their flat bottoms became the tops. We then bathed each cake in a bright-white glaze made from vanilla bean, confectioners' sugar, and milk. For a darling touch, decorate the cakes with candied violets. To coarsely grind dried lavender, pound the dried flowers in a mortar and pestle or pulse several times in a spice grinder.
1. For the cakes Adjust oven rack to lower-middle position and heat oven to 325 degrees. Whisk 2 tablespoons sugar and melted butter together in bowl. Brush 12-cup muffin tin with butter-sugar mixture.
2. Whisk flour, salt, baking powder, and baking soda together in bowl. Whisk buttermilk, lavender, and vanilla together in small bowl. Using stand mixer fitted with paddle, beat butter and remaining ⅔ cup sugar on medium-high speed until pale and fluffy, about 3 minutes. Add eggs, one at a time, and beat until combined. Reduce speed to low and add flour mixture in 3 additions, alternating with buttermilk mixture in 2 additions, scraping down bowl as needed. Increase speed to medium-high and beat until completely smooth, about 30 seconds. Give batter final stir by hand.
3. Divide batter evenly among prepared muffin cups and smooth tops. Bake until golden brown and toothpick inserted in center comes out clean, about 15 minutes, rotating muffin tin halfway through baking.
4. Let cakes cool in muffin tin on wire rack for 10 minutes. Invert muffin tin over wire rack and gently tap pan several times to help cakes release. Let cakes cool completely on rack, bottom side up, about 30 minutes. (Unglazed cakes can be stored at room temperature for up to 24 hours.)
5. For the glaze Cut vanilla bean in half lengthwise. Using tip of paring knife, scrape out seeds. Whisk vanilla seeds, sugar, and 2 tablespoons milk together in bowl until smooth. Gradually add remaining 2 tablespoons milk as needed, teaspoon by teaspoon, until glaze is thick but pourable. Spoon glaze over top of each cooled cake, letting some drip down sides. Let glaze set for 10 minutes before serving.