Heat the oven to 325ºF. Coat a bundt pan with 1 tablespoon (13 grams) of the butter and sprinkle with 2 tablespoons (26 grams)of the sugar. Cover the pan tightly with plastic wrap and shake. Place the pan in the refrigerator.
Whisk together 2 1/2 cups (332 grams) of the flour, the baking powder, and salt, in a medium bowl. Set aside.
Cream the remaining butter and sugar together in a stand mixer fitted with the paddle attachment on medium speed for 5 minutes. Add the eggs, one at a time, until fully incorporated. After all 4 eggs are in, scrape down the sides of the bowl, add the vanilla extract, and beat until fluffy, 1 to 2 minutes. Reduce the speed to low, then add the flour mixture to the butter mixture and combine. Do not overbeat.
Combine the blueberries with the remaining 1/2 cup (68 grams) of all-purpose flour in a zip-top bag and shake. Fold the berry and flour mixture into the batter and pour into the prepared pan.
Bake for 1 hour and 15 minutes or until a probe thermometer comes out clean and registers 210 degrees F. Cool in the pan on a cooling rack for at least 15 minutes before depanning and cooling completely.