Preheat the broiler. Spread the mayonnaise on the cut sides of each roll. Place the rolls, cut sides up, on a parchment-lined baking sheet. Broil until just golden, 1 to 2 minutes.
Preheat the oven to 200 degrees . Divide the turkey among the roll bottoms; top with the tomato slices and 2 half-slices of bacon. Place the sheet in the oven to keep the sandwich ingredients warm while making the sauce.
In a small saucepan, melt the butter over medium heat. Whisk in the flour, then the milk, Pecorino Romano and paprika; stir until the sauce thickens, 4 to 5 minutes. Remove from the heat, add the cheddar and stir until melted. Season the cheese sauce with salt and pepper.
Place the sandwich bottoms on a platter and drizzle with the cheese sauce (about 1 tbsp. each); add the roll top. Serve warm.