Heat oven to 350°F. Grease and line a 9×13-inch pan with parchment.
Whisk flour, baking powder, baking soda, 0.75 tsp salt, cinnamon, nutmeg, and allspice in a bowl.
Stir granulated sugar and brown sugar with melted butter until glossy and smooth.
Beat in eggs and 2 tsp vanilla until the mixture looks creamy.
Whisk in applesauce and buttermilk until combined.
Fold dry ingredients into wet just until no dry spots remain. Do not overmix.
Gently fold in diced apples and pecans, then scrape batter into the pan and smooth the top.
Bake until golden and a tester comes out clean, 40 to 48 minutes. Cool 10 minutes.
Make the caramel: melt 0.5 cup butter in a saucepan over medium heat. Stir in 0.75 cup brown sugar.
Simmer 2 minutes, whisking. Slowly add cream and 0.5 tsp salt. Cook 3 to 5 minutes until slightly thickened.
Remove from heat and stir in 1 tsp vanilla. Let the caramel stand 2 minutes to settle.
Poke the warm cake all over with a skewer. Pour caramel evenly on top and spread to the edges.
Rest 20 minutes to set. Slice, garnish with extra pecans if desired, and serve warm.