In a medium mixing bowl, whisk flour, baking powder, baking soda, and salt.
Melt butter, stir in oil, and let cool.
In a large bowl, whisk egg, milk, sour cream, and vanilla until smooth. Whisk in butter mixture.
Fold dry ingredients into wet until just combined. Let rest 15 minutes if you have the time. Preheat oven to 375 F and grease donut pan.
Drop jam onto batter and swirl gently with a knife or chopstick. Transfer to piping bag and pipe into pan, filling wells ¾ full.
Bake 8 to 10 minutes until tops spring back when touched. Cool 5 minutes, then transfer to rack.
For glaze: Whisk powdered sugar with milk until smooth. Add jam, swirl lightly. Dip donuts into glaze, twist for marble effect, and let set 10 minutes.