Melt 1 tablespoon butter in a skillet over medium-low heat. Cook red onion for 15 to 20 minutes, stirring often, until soft and golden at the edges.
Add chopped turkey, broth and Worcestershire, cover and warm gently for 5 to 8 minutes until the meat reaches 165°F. Uncover to evaporate excess loose liquid.
Heat the oven to 350°F. Split the connected rolls horizontally and place the bottom slab in a lined 9-by-13-inch pan. Add half the cheddar, spread warm turkey-onion filling evenly over it and add remaining cheddar and roll tops.
Melt remaining butter and mix with garlic powder and pepper. Brush over the tops, cover loosely with foil and bake for 10 minutes.
Uncover and bake for 5 to 8 minutes until the tops are golden, cheese melts and the center remains at least 165°F. Rest for 3 minutes and cut into 12 sliders, serving 2 per person.