Preheat oven to 375°. In a cold Dutch oven or high-sided skillet, place bacon. Cook over medium-high heat, stirring occasionally, until fat is rendered and bacon is crisp, 12 to 14 minutes. Using a slotted spoon, transfer to a paper towel-lined plate, reserving 2 tablespoons drippings in pot.

In same pot over medium low heat, cook onion and garlic, stirring occasionally, until softened, about 7 minutes; season with a pinch of salt. Whisk in flour and cook, whisking constantly, until fragrant and golden brown, 2 to 3 minutes.

Meanwhile, in a small heatproof bowl, microwave milk until warmed through, about 1 minute. While whisking, slowly add milk to roux, whisking until smooth. Stir in mustard and paprika; season with salt and pepper. Continue to cook over medium-low heat, whisking constantly, until sauce thickens, about 2 minutes. Remove from heat and whisk in egg yolk.

Fold in Gruyère and cheddar and cook, stirring and reducing heat to low if needed, until cheese is melted, about 2 minutes.

Spray a medium baking dish with cooking spray. Slice rolls still attached to each other parallel to work surface. Place bottom half in prepared dish and top with turkey. Pour cheese sauce over turkey and layer with bacon and tomato slices. Close with top half of rolls. Brush rolls with butter. Sprinkle with everything bagel seasoning.

Bake sliders until golden brown, 10 to 12 minutes. Cut into 12 pieces to serve.