Adjust oven rack to upper-middle position and preheat oven to 425 degrees. Spray a standard muffin tin with non-stick cooking spray.
Bring 1 cup of the blueberries and 1 teaspoon of the sugar to a simmer in a small saucepan over medium heat. Cook, mashing berries with a large spoon several times and stirring frequently, until berries have broken down and mixture is thickened and reduced to ¼ cup, about 6 minutes. Transfer to a small bowl and cool to room temperature, 10 to 15 minutes.
Whisk the flour, baking powder, and salt together in a large bowl. Whisk the remaining 1⅛ cups sugar and the eggs together in a medium bowl until thick, about 45 seconds. Slowly whisk in the melted butter and oil until combined. Whisk in buttermilk and vanilla until combined. Using a rubber spatula, fold the egg mixture and remaining cup of blueberries into the flour mixture until just moistened. (Batter will be very lumpy with few spots of dry flour; do not overmix.)
Divide the batter equally among the prepared muffin cups (the batter should completely fill the cups and mound slightly). Spoon 1 teaspoon of the cooked blueberry mixture into the center of each mound of batter. Using a skewer, gently swirl the filling into the batter using a figure-eight motion. Sprinkle the sugar evenly over muffins.
Bake until the tops of the muffin are golden and just firm, 17 to 19 minutes, rotating the muffin tin from front to back halfway through the baking time. Cool the muffins in the tin for 5 minutes, then transfer to a wire rack and cool for 5 minutes before serving. The muffins can be stored in an airtight container at room temperature for up to 4 days, or wrapped individually with plastic wrap, placed in a freezer bag, and frozen for up to 2 months.
Note: If you must substitute for the buttermilk, use ¾ cup plain whole-milk or low-fat yogurt + ¼ cup milk.Nutritional values are based on one muffin