Brush a large bowl with 2 tablespoons of the garlic butter and 1 tablespoon of neutral oil. Set aside 4 tablespoons of the garlic butter for brushing onto the brioche rolls once baked.
Line a large baking sheet with parchment paper. Set aside.
Add the yeast mixture, sugar, and 2½ cups of bread flour to the paste in the electric mixer bowl. Using the dough hook, mix of low speed until the dough looks shaggy. Increase the speed to medium and add in 2 eggs (one at a time) and the 1 egg yolk. Note: The remaining egg will be used later for the egg wash.
Add in the sea salt and allow the dough to mix on medium speed until a massive ball is formed (approx 2-3 minutes). Decrease the speed to low and add in the 2 remaining tablespoons of garlic butter (one at a time). Once fully incorporated add in 4 tablespoons of unsalted butter, again one at time. Increase the mixer speed back to medium and allow the dough to mix until smooth and soft (approx 8-11 minutes).
Remove the dough from the mixer, form a nicely shaped ball and place the dough into the greased bowl. Cover the bowl with plastic wrap and allow the dough to rest in a warm area for 1-2 hours or until it doubles in size.
Punch the dough and knead for 2 minutes to deflate the dough. Next, weigh the dough and based on that number divide the dough equally into 15 pieces (weighing 48-60 grams each). Working with one piece at a time, cover the rest with plastic wrap to prevent the dough from drying out. In a clean working space, fold the edges of the dough underneath and pinch the bottom to seal the roll. Turn the dough at 90 degree angles while constantly pinching and folding the dough. Continue this process until the dough looks smooth with only seams at the bottom of the roll. Place the palm on your hand directly on top of the roll and rotate the dough in a circular motion. Then, push the dough forward and backwards (push it away from you then bring the dough towards you). Repeat this process for 1 minute. Transfer this round dinner roll onto the lined parchment paper. Continue this process for the remaining 14 pieces.
Spread out the dinner rolls on the baking sheet. The dinner rolls should have a little distance between each other. Loosely cover the pan with plastic wrap and allow the rolls to proof in a warm area (double in size) for 45 minutes to 1 hour. During this process, you'll notice the rolls bonding together and becoming friends. Once this happens you're ready to bake.
Preheat the oven to 350 degrees F. Beat the remaining egg and 1 tablespoon of whole milk together. Push the egg wash gently on top of the rolls. Bake the dinner rolls until deep golden brown 20-30 minutes.
Transfer the pan onto a wire rack and brush the warm rolls with the remaining garlic butter (4 tablespoons). Sprinkle flaky sea salt on top.
Serve warm. Enjoy.