Heat the oven to 350°F. Mix ground chicken, egg, breadcrumbs, Parmesan, salt and oregano just until combined, then shape into 12 small patties about 1/2 inch thick.
Heat oil in a large skillet over medium heat and cook patties in 2 batches for 3 to 4 minutes per side until each reaches 165°F.
Split the connected Hawaiian rolls horizontally and place the bottoms in a parchment-lined 9-by-13-inch pan. Arrange one cooked patty over each roll.
Spoon marinara evenly over the patties, add mozzarella and replace the top slab. Brush with butter mixed with garlic powder.
Cover with foil and bake for 15 minutes, then uncover for 8 to 10 minutes until the center reaches 165°F and the cheese melts.
Rest for 5 minutes and cut along the seams into 12 sliders.