PREHEAT oven to 350°.
LIGHTLY spray a 13x9x2-inch baking pan with baking spray and flour; set aside.
IN a medium bowl, whisk together flour, baking powder, and salt. Set aside.
IN a large bowl, beat butter and sugar at high speed with an electric mixer until light and fluffy, approximately 5 minutes. Add eggs, one at a time, beating well after each addition. Add vanilla, stirring to combine.
WITH mixer at lowest speed, add flour mixture in 3 batches, alternating with half-and-half and beating until smooth. Spread batter in prepared pan.
BAKE until a wooden pick inserted near the center comes out clean, 25 to 35 minutes. Remove from oven. Using a wooden spoon handle, poke several holes in warm cake. Pour 1 jar prepared caramel topping over cake. Let cake sit at room temperature to absorb caramel, and cool completely, approximately 2 hours.
IN a large bowl, combine cream cheese and vanilla. Beat at medium-high speed with an electric mixer until creamy, approximately 2 minutes. Add confectioners’ sugar, beating until smooth. Spread over cooled cake (refrigerate leftover). Pour remaining 1 jar caramel topping over frosting in a zigzag pattern. Drag a butter knife through caramel topping to created desired design. Store tightly covered in the refrigerator up to 5 days.