Whisk eggs, salt, and pepper together in a bowl until frothy. Melt 2 tablespoons butter in a large skillet over medium-low heat. Pour eggs into skillet; cook and stir with spatula until set, 3 to 6 minutes. Remove from heat.
Cut rolls in half horizontally; lay bottoms in a single layer in a 9×13-inch baking dish. Add a layer of provolone cheese, then scrambled eggs, then a layer of ham, then provolone cheese, then ham, then provolone cheese again. Cover with roll tops. Cut through ham and provolone cheese layers to make individual sandwiches.
Melt 1/4 cup butter, brown sugar, and mustard together in a small saucepan over medium heat; cook and stir until sugar is dissolved. Spread mixture over roll tops. Cover baking dish with aluminum foil and let stand, about 30 minutes.
Preheat oven to 350 degrees F (175 degrees C). Remove aluminum foil from baking dish.
Bake in preheated oven until tops are golden brown and cheese has melted, 15 to 20 minutes.
Number of servings depend on the number of rolls in the package.
Sliders can be assembled ahead of time and baked just before serving, if desired.
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