Preheat the oven to 350°F. Prepare a parchment paper sling for a 13x9 baking pan and spray with nonstick baking spray.
Whisk the flour, baking powder, and salt together in a bowl.
In a medium bowl, whisk the brown sugar and melted butter together until fully combined. Whisk in the eggs and vanilla.
Using a rubber spatula, gently fold in the flour mixture. Once combined, fold in the white chocolate chips and set aside.
Add the caramel bits and heavy cream to a microwave-safe bowl. Microwave at 50% power in 30-second increments, stirring after each, until smooth. Let cool slightly (not thick and hard, but not piping hot).
Scrape the batter into the prepared pan and smooth the top.
Drizzle the slightly cooled caramel over the batter. Use a knife to create a marbled swirl, running it in the opposite direction of the drizzle.
Bake until the top is shiny and slightly cracked and feels firm (not jiggly), about 30 to 35 minutes, rotating the pan halfway through.
Immediately after removing from the oven, top with a generous pinch of flaky sea salt.
Let cool in the pan for 10 minutes, then remove and cool completely on a wire rack before cutting into bars.