Make the lemon sugar by stirring the white sugar with the lemon zest together in a small bowl; set aside.
Make sure the oven rack is in the upper-middle position. Preheat the oven to 425 degrees and coat a muffin tin with cooking spray.
Make the jam by bringing 1 cup of blueberries and 1 teaspoon of sugar to simmer in a small saucepan over medium heat.
Cook, mashing the berries with a spoon several times and stirring them frequently, until the blueberries have broken down and the mixture is thickened and reduced to about 1/4 cup, about 6-8 minutes. Transfer jam to a small bowl and cool to room temperature.
Make the muffins by whisking the flour, baking powder and salt together in a large bowl.
In a separate bowl, whisk the sugar and eggs together until thick and creamy, about 45 seconds.
Slowly whisk in the butter and oil until combined. Whisk in the buttermilk and vanilla until combined.
Using a rubber spatula, fold the egg mixture and blueberries into the flour mixture until just moistened. Don't overmix.
Divide the batter evenly in the prepared muffin tin. Batter should fill the cups and be slightly mounded.
Spoon a teaspoon of the cooled jam in the center of each mound of batter. Using a wooden skewer, gently swirl the berry jam into batter using figure-eight motion.
Sprinkle the lemon sugar evenly over the muffins.
Bake until the muffin tops are golden and just firm, 16-18 minutes, rotating muffin halfway through baking time.
Remove and cool muffins in the tin for 5 minutes before transferring to a rack to cool for another 5 minutes.