Preheat the oven to 425F. Line a standard 12-cup muffin pan with 6 muffin liners.
Add the butter to a saucepan over medium-high heat. Allow to melt and brown, stirring continuously (~5-8 minutes).
Once the brown butter reaches a deep golden amber color and smells nutty, remove from heat and pour into a large bowl. Set aside to cool slightly (about 15-20 minutes).
Prepare the cream cheese filling by beating the cream cheese to smooth, then beat in sugar, vanilla, and salt for about 2 minutes until very smooth and creamy.
For the oat streusel, combine the flour, oats, brown sugar, cinnamon, and butter in a medium bowl. Mix until crumbly.
In a medium bowl, whisk together the flour, baking powder, baking soda, cinnamon, pumpkin pie spice, and salt.
To the bowl with the cooled brown butter, add the brown sugar, eggs, pumpkin puree, Greek yogurt or sour cream, and vanilla. Whisk until well combined.
Add the dry ingredients to the wet, and fold until just combined. Cover the bowl and allow the batter to rest for 15 minutes.
Scoop and divide the batter among the prepared muffin cups, filling them to the rim.
Pipe the cream cheese filling into the center of the batter for each muffin.
Sprinkle the oat streusel on top of the muffins.
For regular-sized muffins: bake at 425F for 5 minutes, then turn the oven down to 350F and bake for another 15-18 minutes.
For jumbo muffins: bake at 425F for 5 minutes, then turn the oven down to 350F and bake for another 25-28 minutes.
Remove the muffins from the oven and allow them to cool in the pan for 5 minutes.
Pipe extra cream cheese filling into each muffin before serving.
