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.

Whisk flour, salt, baking powder, and baking soda together in bowl; set aside.

Process lavender in spice grinder until coarsely ground, about 15 seconds; transfer to small bowl and whisk in buttermilk and vanilla.

Using stand mixer fitted with paddle, beat remaining 6 tablespoons 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 dough final stir by hand to ensure that no flour pockets remain.

Divide batter evenly among prepared muffin cups and smooth tops.

Bake until golden brown and toothpick inserted in center of cake comes out clean, about 15 minutes, rotating muffin tin halfway through baking.

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 on rack, bottom side up, until completely cool, about 30 minutes.

Cut vanilla bean in half lengthwise. Using tip of paring knife or spoon, scrape out seeds.

Whisk vanilla seeds, sugar, and 2 tablespoons milk together in bowl until smooth.

Gradually add remaining 2 tablespoons milk as needed, 1 teaspoon at a time, 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.