For the Jam
Bring 1 cup of blueberries and 1 teaspoon of sugar to a simmer in a small saucepan over medium heat. Cook the berries, mashing with a spoon several times to break some of the berries open.

Stir frequently until mixture is thickened and reduced to about a 1/4 cup (about 6 minutes).

Transfer to small bowl and cool to room temperature, 10 to 15 minutes.

For the Muffins
Preheat oven to 425F. Spray muffin tin with nonstick cooking spray.

Whisk flour, baking powder, and salt together in large bowl.

Whisk 1 1/8 cups sugar and eggs together in a medium bowl until thick and texture is consistent (about 45 seconds).

Slowly whisk in butter and oil until combined. Whisk in the buttermilk and vanilla until combined.

Using a rubber spatula, fold the egg mixture and the remaining cup of blueberries into the flour mixture until just moistened (batter will be very lumpy with a few spots of dry flour; do not overmix).

Divide the batter equally among the prepared muffin cups (batter should completely fill cups and mound slightly).

Spoon a teaspoon of jam into center of each mound of batter. Use a chopstick or skewer to gently swirl the berry jam into the batter using figure-eight motion.

Bake until the muffin tops are golden and just firm, about 17 to 19 minutes rotating muffin tin from front to back halfway through baking. Cool muffins in muffin tin for 5 minutes, then transfer to wire rack and cool 5 minutes before serving.