Preheat the oven to 400°F (200°C). Line 12 standard muffin cups with paper liners.
Whisk together the flour, sugar, brown sugar, baking powder, baking soda, and salt. Make a well in the center of the mixture.
In a separate bowl, stir together the melted butter, peanut butter, milk, sour cream, eggs, and vanilla. Pour into the well in the flour mixture, and stir just until combined or a few small streaks of flour remain.
Divide the batter among the prepared muffin cups, filling each cup about 3/4 full.
Place 1/4 to 1/2 teaspoon of jelly on top of each muffin. Use a thin knife to swirl into the muffin batter. If you like, sprinkle the tops with a pinch of coarse sugar.
Bake 14 to 18 minutes, or until the muffins are golden brown and a pick inserted into the center comes out clean.
Cool the muffins in the pan on a wire rack for 10 minutes. Then transfer the muffins from the pan directly onto a rack to continue cooling.
Notes
Store in an airtight container at room temperature up to 3 days or in the freezer up to 3 months.