Adjust the oven rack to upper 1/3 of oven and Preheat oven to 425°F. Lightly grease muffin tin or use cupcake liners.
To make blueberry swirl - In a small saucepan over medium heat, bring 1 cup of the blueberries and 1 teaspoon of the sugar to a simmer. Continue to cook while mashing/squishing the berries with a spoon and stirring until the berries have broken and the mixture is thick and reduced to around a fourth of a cup. Allow mixture to cool to room temperature, 10 to 15 minutes.
While mixture is cooling, In a large bowl, whisk the flour, baking soda and salt- set aside.
In a medium bowl whisk the remaining 1 and 1/8 cup of sugar and eggs until evenly mixed and thick, around 45 seconds. Whisk in the melted butter and oil until combined. Whisk in the buttermilk and vanilla until combined.
*With a rubber spatula, gently fold the wet mixture and the remaining blueberries into the dry ingredients. Fold just until the mixture is moistened- a few remaining flour spots are fine as you don't want to over mix the batter.
Using an ice cream scoop, evenly divide the batter between the muffin cups, the muffin cups will be completely full. (I sometimes end up with 13 or 14 muffins and use a second pan)
Divide the cooked blueberries between the muffins- around a heaping teaspoon each muffin. Just dollop it on the top. Then take a small knife or skewer and gently swirl the mixture into the muffin, with a figure 8 motion.
Sprinkle the lemon sugar mixture evenly on top of the muffins
Bake the muffins in the preheated oven, rotating pan once, until tops are just firm to touch and golden, about 17-19 minutes. Remove from oven and cool in pan for about 5 minutes. Remove muffins from pan and place on cooling rack (you may need to gently release muffins with a knife if they stick.)