Butterscotch Pecan Cake with Butterscotch Frosting

Vegetable oil cooking spray, for pans

All-purpose flour- 3¾

Baking powder- 1¼

Baking soda- 3/4

Coarse salt- 2½

Unsalted butter, softened- 10 ounces (2½ sticks)

Packed dark-brown sugar- 2½

Eggs, room temperature- 4 large

Pure vanilla extract- 1 tablespoon plus 1 teaspoon

Buttermilk, room temperature- 1¼

Packed dark-brown sugar-

Butter, cut into pieces- 1½ ounces (3 tablespoons)

Light corn syrup- 1/4

Coarse salt- 1/8

Heavy cream- 1/4

Unsalted butter (1 stick left whole, 2 sticks cut into small pieces, softened) - 12 ounces, (3 sticks)

Packed dark-brown sugar- 2

Heavy cream- 1

Coarse salt- 1/2

Cream cheese, softened- 20

Confectioners' sugar, sifted- 1/2

pecan halves, toasted and chopped, plus more halves for garnish