Preheat the oven to 350°F (175°C). Grease a 12-cup muffin tin or mini bundt pan thoroughly, dust lightly with flour, and tap out the excess. Line muffin cup bottoms with parchment circles if desired.
In a medium bowl, whisk together the flour, cornstarch, baking powder, and 1/2 teaspoon salt until well combined; set aside.
In a small measuring cup or bowl, stir together the milk or buttermilk and 1/4 cup lemon juice; let sit a few minutes while you prepare the batter.
In a large mixing bowl, beat the softened butter and granulated sugar with a hand mixer on medium speed until very pale and fluffy, 3–5 minutes, scraping down the bowl as needed.
Add the lemon zest directly over the butter-sugar mixture so the oils fall into the bowl, then beat again to distribute the zest evenly. Beat in the vanilla extract if using.
Add the eggs one at a time, beating well after each addition and scraping down the bowl, until the mixture is smooth and slightly thick.
Add one-third of the flour mixture to the butter mixture and mix on low just until combined. Add half of the lemon-milk mixture and mix gently. Repeat with another third of the flour, the remaining lemon-milk, then the final third of flour, mixing on low or by hand just until no dry streaks remain.
Check the batter consistency; it should be smooth and fall in thick ribbons from a spoon. If it seems very stiff, gently fold in an extra tablespoon of milk, taking care not to overmix.
Spoon or scoop the batter into the prepared pan, filling each cavity about two-thirds full. Smooth the tops lightly with the back of a spoon for even baking.
Bake for 15–20 minutes, or until the tops are lightly golden, the cakes spring back when gently pressed, and a toothpick inserted in the center comes out clean.
Let the cakes cool in the pan for 5–10 minutes, then carefully loosen the edges with a thin knife and transfer to a wire rack to cool completely before glazing.
While the cakes cool, warm the 1/4 cup cream or milk in a small saucepan or microwave-safe bowl until steaming but not boiling. Stir in the dried lavender, cover, and let steep for 5–10 minutes, depending on how strong you want the flavor.
Strain the lavender-infused cream through a fine mesh sieve into a clean bowl, pressing gently on the lavender to extract the liquid; discard the solids.
In a medium bowl, whisk 1 1/2 cups powdered sugar with 2–3 tablespoons of the warm lavender-infused cream, 1 tablespoon lemon juice, and a pinch of salt if using. Add more infused cream or lemon juice a teaspoon at a time until the glaze is smooth and flows in a slow ribbon from the whisk. If too thin, whisk in additional powdered sugar.
Place the cooled mini cakes on a wire rack set over a sheet of parchment or a tray. Spoon the lavender glaze over the tops of each cake, letting it drip down the sides. For a more opaque finish, let the first layer set slightly, then add a second spoonful of glaze.
Allow the glaze to set for at least 15–20 minutes before serving. Serve at room temperature.