Preheat the oven to 350°F (175°C). Line a rimmed baking sheet with parchment paper for the bacon and set a separate large rimmed baking pan or sheet for warming assembled sliders.

Arrange the bacon slices in a single layer on the prepared parchment-lined baking sheet. Bake for 15–20 minutes, turning once if needed, until the bacon is crispy and browned at the edges. Transfer cooked bacon to a paper towel–lined plate to drain.

While the bacon bakes, separate the slider buns and arrange the tops and bottoms on the warming sheet in two neat rows. Lightly butter the cut sides of the buns with the softened butter. If you prefer a shinier top, brush a light coat of melted butter on the outside of the tops as well.

Make the eggs: in a medium bowl, lightly beat the eggs with the milk or cream (if using), 1/4 teaspoon kosher salt, and 1/8 teaspoon freshly ground black pepper until blended. Heat a nonstick skillet over medium-low heat and add 1 tablespoon vegetable oil, swirling to coat.

For folded/fried eggs that hold together: pour half of the beaten egg into the skillet and swirl to create an even, thin layer. Cook gently for 1–2 minutes until the edges set but the surface is still slightly wet. Using a spatula, carefully fold the cooked edge toward the center, allowing the uncooked egg to spread into the space. Repeat folding until the egg is mostly set but still a little soft in the center—aim for a tender interior with a slight runniness. Slide the folded egg onto a plate. Repeat with the remaining egg mixture to make two larger folded eggs, then slice each folded egg into six pieces to give you twelve portions.

Alternative egg method (individual fried eggs): if you prefer distinct fried eggs, heat the skillet over medium, add a small amount of oil or spray, crack 8 eggs into the pan in batches so they don’t touch, and cook until whites are set and yolks are still a touch runny (about 2–3 minutes). Season lightly with salt and pepper and transfer eggs to a plate.

Assemble the sliders on the warming sheet: place the bottoms of the buns in two neat rows. Top each bun bottom with a half slice of cheese so the cheese will melt directly onto the warm egg and bacon.

Layer the egg portions on top of the cheese halves—one folded or fried portion per slider. If your eggs are larger and need trimming to fit, gently fold or quarter them so they sit comfortably within the bun.

Add a strip of crisp bacon to each slider. If your bacon strips are longer than the buns, fold them in half before placing so they don’t protrude.

Place the bun tops on each slider, buttery side down toward the filling or shiny-side up as desired. If you’re assembling the sliders for an oven finish, insert a toothpick through the center of each sandwich to keep layers aligned while the cheese melts.

Finish in the oven: slide the assembled sliders into the preheated 350°F (175°C) oven for 6–8 minutes, or until the cheese is melted and the buns are warmed through. For a browned top, switch the oven to broil for 30–45 seconds while watching closely; remove immediately when the tops reach your desired color.

Remove the sliders from the oven and sprinkle the tops with the finely chopped fresh parsley or chives. Let the assembled sliders rest for 1–2 minutes so the cheese sets slightly, then serve warm with hot sauce or ketchup on the side if desired.

Optional make-ahead and reheat tip: if you’re prepping earlier, assemble the sliders without inserting toothpicks, cover them tightly with foil, and refrigerate for up to 24 hours. Reheat covered at 325°F (160°C) for 10–15 minutes, then broil 30 seconds if you want a toasted finish.