Make Brioche Rolls - Start by blooming the yeast. Combine together ⅔ cup of warm milk, 1 teaspoon white sugar and 2 ¼ teaspoons active dry yeast and let it sit for 5 to 7 minutes. Mixture is ready when the surface is foamy.
Combine All Dough Ingredients - In the bowl of a stand mixer, add all-purpose flour, salt, butter, remaining white sugar, eggs and bloomed yeast mixture. With a spoon or spatula, mix the ingredients until it becomes a shaggy ball.3 ¼ Cup (390g) All-Purpose Flour, 1 ½ Teaspoons Fine Salt, 2 Whole Large Eggs, 2 Tablespoons White Sugar, 2 Whole Large Eggs Knead the Dough - Fit your stand mixer with the dough hook attachment and knead the dough on medium speed for about 15 minutes. It's ready when it passed the window pane test. See note below.
Let Double in Size - Cover the bowl with plastic wrap and let the dough rise in a warm place for about an hour or until it doubles in size.
Divide the Dough - Using a kitchen scale, weigh the entire dough and then divide by 12. Each dough ball weighed about 61 grams each for me.
Shape the Rolls - Cover your dough balls with plastic wrap or a kitchen towel to prevent them from drying out. Working one dough ball at a time, press it flat to get rid of any air bubbles. Gather and pinch the edges together and then place it on your work surface seam side down. Form your hand into a relaxed “claw” shape and cup it over the ball of dough. Then move your hand in small circular motions, gently dragging the ball along until smooth. Place it back under the plastic wrap and shape the rest of your buns.
Roll into Logs - Using a rolling pin, roll the dough ball into roughly a 6-inch long, by 4-inch wide (15x10 cm) oval. Starting at the top end, tightly roll the dough towards yourself to form a log. Pinch the seam to seal the edges, including the ends. Each log should be no longer than 4 inches long, in order to fit in our pan.
Transfer the rolls into a buttered 9x13 inch (22x33 cm) baking pan. Position 4 across, widthwise and 3 down, lengthwise. See photo for reference. Alternatively, you can use a large baking tray, placing them about 1 inch (2.5 cm) apart.
Proof - Allow to proof in a warm place for about 30 to 45 minutes or until doubled in size.
Preheat Oven - With 15 minutes left of proofing, preheat the oven to 375º (190ºC).
Bake - When doubled in size, lightly brush the tops of the brioche buns with a beaten egg and then sprinkle with white sesame seeds. Bake for 16 t0 20 minutes or until the tops are a deep golden brown color. As soon as it comes out of the oven, immediate brush the tops with a tablespoon of melted butter. Let sit in the pan for a few minutes and then transfer to a wire rack to cool completely.
Make Olive Topping - In a small bowl, add olives, pepperoncini peppers, shallot, parsley, basil, thyme, grated garlic, extra-virgin olive oil, balsamic vinegar, honey and black pepper to taste. Place in the fridge for 20 minutes to allow the flavors to mellow out.½ Cup Finely Diced Green Olives½ Cup Finely Diced Kalamata Olives3 Finely Chopped Pepperoncinis1 Tablespoon Finely Chopped Shallot1 Tablespoon Finely Minced Fresh Parsley, 2 Teaspoons Finely Minced Fresh Basil, A Sprig Fresh Thyme1 Garlic Clove¼ Cup Extra-Virgin Olive Oil2 Tablespoons Balsamic Vinegar1 Teaspoon of Honey¼ Teaspoon Black Pepper Assemble Sandwiches - Using a sharp knife or serrated knife, cut the rolls down the middle (or from the side). For the first sandwich variation, I filled 6 rolls with a half slice of provolone cheese, 1 or 2 slices of mortadella, 3 slices of salami and olive topping. For the second variation, I filled the remaining 6 rolls with with provolone, 1 to 2 slices of black forest ham, 3 slices of pepperoni and olive topping. Serve and enjoy!