Preheat the oven to 350°F and grease two 1-pound loaf pans with cooking spray or butter.
In a medium bowl, whisk together the brown sugar, flour, baking powder, and salt until evenly combined.
In a large bowl or using a stand mixer, beat the eggs, milk, and vegetable oil until thoroughly combined.
Gradually add the dry ingredients to the wet mixture, stirring gently until just combined.
Divide half of the batter evenly between the two prepared loaf pans, spreading it to cover the bottom.
In a separate bowl, beat the softened cream cheese, granulated sugar, and egg until smooth and uniform.
Spoon the cream cheese mixture in a continuous line down the center of the batter in each loaf pan.
Distribute the remaining batter over the cream cheese filling in each pan, gently spreading to completely cover.
Drizzle 2 tablespoons of caramel sauce in a stripe on top of each loaf and gently swirl with a knife.
Bake the loaves for 50 minutes, or until a toothpick inserted comes out mostly clean.
Allow the loaves to cool in the pans for 10 minutes, then transfer to a wire rack to cool completely before slicing.