Chop the butter into pieces and place in a microwave-safe bowl. Microwave the butter on high power until just melted and allow to cool slightly.
While the butter is cooling, combine the flour, baking powder, and salt in a medium bowl. Set aside.
Stir together the melted butter with both sugars. Beat in the egg. Add half & half, milk, and vanilla and stir to thoroughly combine.
Add the dry ingredients, stirring just until moistened
Put half the batter into 12 muffin cups using a spoon or a cookie scoop. Add a generous 1 tsp of jam in center of each muffin and swirl with a toothpick. Fill the muffin cups with the remaining batter and swill again with a toothpick. Muffin cups will be nearly full.
Bake for 17-20 minutes or until muffins are lightly browned and spring back when lightly touched.