Preheat the oven to 350°F. Line a 9x13-inch baking pan with foil and spray the foil with cooking spray; set the pan aside.
Break the 1 (8‑ounce) can of almond paste into pieces and place in a food processor. Pulse until the almond paste becomes fine crumbs.
Measure out 1 cup of the almond paste crumbs and set it aside for the crust. Reserve the remaining almond paste crumbs for the filling.
In the bowl of an electric mixer fitted with the paddle attachment, combine the reserved 1 cup almond paste crumbs, 1/2 cup softened butter, and 1/4 cup sugar. Beat on medium speed until light and fluffy.
With the mixer on low, add 1 1/2 cups all-purpose flour gradually and mix just until the dough is crumbly but holds together when pressed.
Press the crumb mixture evenly into the prepared 9x13 pan to form the crust (use the bottom of a measuring cup or your hands to press firmly). Bake the crust for 15 minutes. Remove from the oven but leave the oven on.
While the crust bakes, combine the remaining almond paste crumbs with the 1 (14‑ounce) can of sweetened condensed milk in a medium microwave-safe bowl. Microwave for 30 seconds, then stir until evenly combined and smooth.
When the crust comes out of the oven, evenly sprinkle 1 1/2 cups white chocolate chips and 1 1/2 cups sliced almonds over the hot crust.
Pour the sweetened condensed milk–almond paste mixture over the chips and almonds. Gently spread it into an even layer with a spatula, taking care not to displace the toppings.
Return the pan to the oven and bake for 20 minutes, or until the edges begin to brown.
Remove from the oven and cool completely in the pan on a wire rack. Once fully cooled, lift the bars out using the foil and cut into bars.