Caramel Cake

Preheat oven to 350u0b0F with rack in middle. Butter an 8-inch square cake pan and line with a square of parchment paper, then butter parchment.
Sift together flour, baking powder, baking soda, and salt.
Beat butter and sugar in a large bowl with an electric mixer at medium speed until pale and fluffy, then beat in vanilla. Add eggs 1 at a time, beating well after each addition. At low speed, beat in buttermilk until just combined (mixture may look curdled). Add flour mixture in 3 batches, mixing until each addition is just incorporated.
Spread batter evenly in cake pan, then rap pan on counter several times to eliminate air bubbles. Bake until golden and a wooden pick inserted in center of cake comes out clean, 35 to 40 minutes. Cool in pan on a rack 10 minutes, then run a knife around edge of pan. Invert onto rack and discard parchment, then cool completely, about 1 hour.
Bring cream, brown sugar, corn syrup, and a pinch of salt to a boil in a 1 1/2-quart heavy saucepan over medium heat, stirring until sugar has dissolved. Boil until glaze registers 210 to 212u0b0F on thermometer, 12 to 14 minutes, then stir in vanilla.
Put rack with cake in a shallow baking pan and pour hot glaze over top of cake, allowing it to run down sides. Cool until glaze is set, about 30 minutes.