Make the dinner rolls: Heat milk in the microwave until a little bit hot to the touch. Add in a large bowl with the dried yeast and 1 tbsp sugar. Cover and allow to sit for 5-10 minutes to activate the yeast (it should foam and bubble up a bit). Add remaining sugar, egg, flour, salt and softened unsalted butter and mix until it starts to pull away from the sides of the bowl. The dough should be soft and a little bit sticky. If the dough seems too wet, add 1 tbsp flour at a time until you can work with it. Knead on a lightly floured surface for 2 minutes until a smooth ball forms.
Rise the dough: Lightly grease the same bowl with a little bit of oil and coat the dough in it. Cover the bowl with a clean kitchen towel, aluminum foil or plastic wrap and place it in a warm place. Let it rise for 1-2 hours or until doubled in size. Grease a 9 by 13 inch baking pan or two 9 by 9 inch square or round baking pans. When the dough is ready, punch the dough down to release the air. Divide the dough into 13-16 equal pieces. Shape each piece into a smooth ball using your hands - strech the top and pinch the bottom to seal it. Place the shaped pieces in the baking pan with a little bit of room to grow. Cover them with a clean kitchen towel , aluminum foil or plastic wrap. Allow to rise until doubled in size, about 1 hour.
Bake the dinner rolls: Preheat oven to 350°F and adjust oven rack to a lower position (so the tops don't burn). Bake for 20-25 minutes or until golden-brown on top. Rotate the pan halfway through. If the tops brown too quickly, loosely cover them with aluminum foil. Remove from the oven and let them cool.
Bake the chicken breast: Preheat oven to 400°F. Arrange chicken breasts on a baking sheet, drizzle with olive oil and season with salt and freshly ground black pepper. Bake for 30-35 minutes or until the internal temperature reaches 165°F. Let it cool down a bit and then shred it with a couple of forks.
Make the BBQ sauce: In a small saucepan mix all the ingredients over medium heat. When it starts simmering, reduce the heat to low and cook until thickened, about 10 minutes.
Make the sliders: Reduce the oven heat to 350°F. Transfer the dinner rolls to a chopping board and slice them horizontally. Place bottom part in the same baking pan. Mix the shredded chicken with BBQ sauce and place on the bottom part of the dinner rolls. Sprinkle grated mozzarella and cheddar cheese evenly over the chicken. Place the top part of the dinner rolls over the cheese and bake for 15-20 minutes or until the cheese has melted. Loosely cover with aluminum foil to prevent burning.
Serving: In a small saucepan add 2 tbsp butter and minced garlic over medum heat. Cook until the garlic starts sizzling. Remove from heat and add dried oregano and chopped fresh parsley. Brush the sliders with garlic herb butter.