Arrange a rack in center of oven; preheat to 350°. Line a standard 12-cup muffin tin with large muffin liners.
In a large bowl, whisk eggs, pumpkin puree, sour cream, brown sugar, granulated sugar, oil, and vanilla until smooth.
In a medium bowl, whisk flour, pumpkin pie spice, baking powder, baking soda, nutmeg, salt, and ginger. Working in batches, gradually add dry ingredients to egg mixture and fold with a rubber spatula until no streaks remain (be careful not to overmix).
Using a spoon or a cookie scoop, scoop batter into prepared cups, filling about four-fifths full.
In a large bowl, using a handheld mixer on medium-high speed, beat egg, cream cheese, granulated sugar, vanilla, and salt until smooth. Transfer filling to a large resealable plastic bag or piping bag.
Twist top of bag closed, then cut 1" off tip of one corner of bag. Insert tip into center of batter. You will feel the bottom of the muffin tin. Using light pressure, slowly fill and guide bag upward and out. Fill until batter slightly overflows; you should have a cream cheese center and a rim of pumpkin muffin batter surrounding it.
Sprinkle rims of batter with pepitas and demerara sugar, leaving cream cheese filling exposed.
Bake muffins until golden brown and center springs back when touched, about 30 minutes. Transfer to a wire rack and let cool slightly.
