Preheat oven to 350 degrees, with rack in lower third. Butter six (1-cup) molds of a mini angel food cake pan or mini bundt pan. Dust with flour, and tap out excess. Pick 2 teaspoons small sprigs from tops of lemon thyme sprigs, and divide evenly among molds; set aside. Coarsely chop remaining lemon thyme leaves to make 2 tablespoons; whisk chopped lemon thyme with the flour, salt, and lemon zest in a small bowl. Set aside.
Put butter into the bowl of an electric mixer fitted with the paddle attachment. Cream on medium speed until pale and fluffy, scraping down sides of bowl as needed, about 4 minutes. Add sugar. Mix until pale and fluffy, scraping down sides of bowl as needed, about 3 minutes.
Mix in vanilla. Add eggs, 1 at a time, mixing well after each addition; mix until smooth. Reduce speed to low. Add flour mixture in 3 batches, mixing until just combined after each addition.
Spoon batter over lemon thyme in prepared molds. Smooth tops using a small rubber spatula. Firmly tap the pan on counter to eliminate any air bubbles. Bake until a cake tester inserted into centers comes out clean, about 40 minutes. Let cakes cool slightly in pan on a wire rack, about 10 minutes. Run a knife around edges of molds to loosen; unmold cakes. Place each cake on a serving plate, and drizzle with about 1 tablespoon syrup. Garnish with lemon thyme sprig.