FOR THE TOPPING: Stir together sugar (3 tablespoons), brown sugar (3 tablespoons), salt, and flour (1/2 cup plus 3 tablespoons) in a small bowl until combined. Drizzle with warm butter (5 tablespoons) and toss with a fork until evenly moistened and the mixture forms large chunks with some pea-sized pieces throughout. Set aside.
FOR THE MUFFINS: Adjust oven rack to upper-middle position and heat oven to 425ºF (218ºC). Spray the standard muffin tin with nonstick cooking spray. Bring 1 cup of blueberries and 1 teaspoon of sugar to simmer in a small saucepan over medium heat. Cook, mashing berries with the spoon several times and stirring frequently until berries have broken down and the mixture is thickened and reduced to ¼ cup, about 6 minutes. Transfer to the small bowl and cool to room temperature, for 10 to 15 minutes.
Whisk flour (2 1/2 cups), baking powder (2 1/2 teaspoons), and salt (1 teaspoon) together in a large bowl. Whisk remaining 1 1/8 cups sugar and eggs (2) together in a medium bowl until thick and homogeneous, about 45 seconds. Slowly whisk in butter (4 tablespoons) and oil (1/4 cup) until combined. Whisk in buttermilk (1 cup) and vanilla (1 1/2 teaspoons) until combined. Using a rubber spatula, fold the egg mixture and the remaining cup of blueberries into the flour mixture until just moistened. (The batter will be very lumpy with few spots of dry flour; do not over mix.)
Following the photos below, use the ice cream scoop or large spoon to divide the batter equally among prepared muffin cups (the batter should completely fill the cups and mound slightly). Spoon a teaspoon of cooked berry mixture into the center of each mound of batter. Using the chopstick or skewer, gently swirl berry filling into the batter using figure-eight motion. Sprinkle streusel topping evenly over the muffins.
Bake until muffin tops are golden and just firm, 17 to 19 minutes, rotating the muffin tin from front to back halfway through baking time. Cool muffins in muffin tin for 5 minutes, then transfer to the wire rack and cool for 5 minutes before serving.