Whisk the flour, baking powder and salt together in a large bowl. Set aside.
In a medium bowl, whisk together 1-1/8 cups sugar and eggs until thick and well combined, about 45 seconds. Slowly whisk in the butter and oil until combined. Nest, whisk in the milk and vanilla until combined.
Using a rubber spatula, fold the egg mixture into the flour mixture until just moistened. The batter will be very lumpy with a few spots of dry flour; do not overmix. (If using whole blueberries, fold in now.)
Fill muffin cups 1/2 full with batter and top each muffin with a teaspoon of the blueberry jam. Use a toothpick to swirl. Divide the remaining batter between muffin cups. The batter should completely fill the cups and mound slightly. Divide the remaining cooked berry mixture between muffin cups. Use a toothpick to swirl.