Preheat the oven to 350°F and spray a square casserole dish with non-stick spray. Lay the buns flat then, without pulling them apart, slice them down the center lengthwise and remove the tops. Place the bottom half in the prepared baking dish and set the tops aside until the end.

Crack the eggs in a large bowl then whisk them together with the milk, salt, and pepper. Melt 1 tablespoon of the butter, vegan butter, or olive oil in a medium to large nonstick skillet over medium-low heat and swirl to coat. Pour the egg mixture into the pan and cook, stirring frequently, until the eggs are just barely cooked, about 5 minutes. They will continue cooking in the oven. Remove from the heat.

Place four slices of cheese on the bottom buns in the casserole dish then fold each quarter piece of ham on top of each bun. This helps make it easy to pull the sliders apart after they're baked. You could leave them whole and lay them across and use a knife to cut through the sliders if you prefer. Top the ham with the scrambled eggs and spread it evenly across the sliders. Finish with one more layer of cheddar cheese, then place the top buns on top.

Quickly whisk together the melted butter, honey, dijon, and everything bagel seasoning then spread it generously on top of the buns. Bake in the preheated oven for 18-20 minutes, until they're heated through and the cheese is melted. Check at 10 minutes and cover them with foil if they’re looking too brown.