Preheat oven to 350 degrees F. Grease twenty-four 2-1/2-inch muffin cups; set aside. In a medium bowl stir together flour, baking powder, cinnamon, baking soda, and salt; set aside.
In a large bowl beat butter with an electric mixer on medium to high speed for 30 seconds. Add granulated sugar and brown sugar, beating until combined. Beat in eggs, pumpkin butter, and vanilla until combined. Stir vinegar into evaporated milk (mixture will look curdled). Alternately add flour mixture and milk mixture to butter mixture, beating on low speed after each addition just until combined. Stir in the 1/2 cup walnuts. Spoon batter into the prepared cups, filling each about three-fourths full.
Bake for 18 to 20 minutes or until a toothpick inserted near centers comes out clean. Cool in pans on wire racks for 5 minutes. Remove from pans. If desired, cool cakes completely on racks.
To serve, place each warm or cooled cake on a dessert plate. If desired, top with broken walnuts. Spoon about 1-1/2 tablespoons of the Caramel Sauce over each cake.
In a medium heavy saucepan combine brown sugar and cornstarch. Stir in half-and-half, the water, and corn syrup. Cook and stir over medium heat until bubbly (mixture might look curdled). Cook and stir for 2 minutes more. Remove from heat. Stir in butter and vanilla. Serve warm.