Preheat the oven to 350°F (175°C). Grease and flour two 9-inch round pans or line them with parchment; set aside.

Infuse the lavender: warm the milk over low heat until steaming (don’t boil). Remove from heat, add 2 tablespoons dried lavender, cover, and steep for 5 minutes. Cool to room temperature, then strain through fine mesh, pressing gently to extract liquid. Discard solids.

Whisk dry ingredients: combine flour, baking powder, baking soda, and salt in a medium bowl. Set aside.

Cream butter and sugar: in a large bowl, beat ½ cup softened butter with 1 ½ cups granulated sugar on medium speed until pale and fluffy, about 3–4 minutes.

Add eggs and citrus: add eggs one at a time, mixing well after each. Stir in 1 tablespoon lemon zest, ¼ cup lemon juice, and 1 teaspoon vanilla.

Combine wet and dry: add dry ingredients to butter mixture in three additions, alternating with the lavender-infused milk (start and end with dry). Mix just until combined—overmixing will toughen the crumb.

Bake: divide batter evenly between pans and smooth tops. Bake 25–30 minutes until a toothpick comes out clean or with a few moist crumbs.

Cool: cool in pans for 10 minutes, then turn out onto a wire rack to cool completely before frosting.

For a quick glaze: whisk 1 ½ cups powdered sugar with 2 tablespoons lemon juice, 1 tablespoon lemon zest and 1 tablespoon very finely crushed lavender until smooth; drizzle over cooled layers.

For buttercream: gently crush 1 tablespoon dried lavender (don’t pulverize to dust). Beat ½ cup softened butter until creamy, gradually add 4 cups powdered sugar, then add 2 tablespoons heavy cream, 2 tablespoons lemon juice, lemon zest and crushed lavender, plus a pinch of salt. Adjust consistency with more cream or sugar. Chill briefly if too soft.