In a medium saucepan, melt ½ cup unsalted butter over medium heat. Once melted, continue cooking, stirring frequently, until the butter foams and then begins to turn a golden brown with a nutty aroma (about 5–7 minutes). Watch carefully to avoid burning.
Remove from heat and transfer the browned butter to a heatproof bowl to cool for 10 minutes.
Once the butter has cooled slightly, whisk in ½ cup granulated sugar and ¾ cup light brown sugar until smooth.
Add in the 2 large eggs, 1 tsp vanilla extract, and ¼ cup whole milk, and whisk until fully combined.
Stir in the 15 oz pumpkin puree until the mixture is smooth and well combined.
In a separate bowl, whisk together the dry ingredients: 1¾ cups all-purpose flour, 1½ tsp pumpkin pie spice, 2 tsp ground cinnamon, 1 tsp baking powder, and ¼ tsp salt.
Gently fold the dry ingredients into the wet mixture until just combined. Be careful not to overmix, as this can make the bread tough.
In a medium bowl, beat together 8 oz room temperature cream cheese, 1 large egg, ¼ cup granulated sugar, and 3 tbsp all-purpose flour until smooth and creamy.
Line a 9×5-inch loaf pan with parchment paper and lightly grease it.
Pour half of the pumpkin bread batter into the pan and smooth it into an even layer.
Spoon the cream cheese mixture on top of the batter, smoothing it out into an even layer.
Pour the remaining pumpkin bread batter over the cream cheese layer, spreading it out to cover completely (do not swirl).
Bake the cheesecake swirl pumpkin bread in a preheated oven at 350°F (175°C) for 65–75 minutes, or until a toothpick inserted into the center comes out mostly clean (it’s okay if the cheesecake layer is slightly jiggly).
Let the cheesecake swirl pumpkin bread cool in the pan for 10 minutes, then transfer to a wire rack to cool completely for at least 1 hour.