Preheat the oven to 425°F (220°C). Arrange a large rimmed baking sheet or ovenproof skillet near the stove. If using a skillet for toasting, have it on medium heat.

Toast bread

Brush both sides of the 4 slices of bread with a thin film of vegetable oil or softened butter. Toast in a skillet over medium heat or in the oven until golden and crisp, about 2–3 minutes per side on the skillet or 6–8 minutes under the broiler, flipping once. Transfer toasted bread to the baking sheet or keep in the oven-safe skillet.

Prepare ham

If the ham steak is larger than you want, cut into pieces sized to layer over each slice of bread (about 4 oz ham per sandwich). Warm the ham briefly in the skillet for 1–2 minutes per side to heat and lightly brown; set aside on a plate.

Make Cheese Sauce

Create roux

In a medium saucepan over medium heat, melt 3 tablespoons butter. Once foaming, add 3 tablespoons flour and whisk continuously for 1–2 minutes to cook out the raw flour taste but avoid browning.

Add milk

Gradually whisk in 2 cups whole milk in a slow stream, whisking constantly to avoid lumps. Continue whisking and bring mixture to a gentle simmer; the sauce will begin to thicken in 3–5 minutes.

Season and finish

Lower heat to medium-low. Whisk in 1 teaspoon Dijon mustard, 1 teaspoon Worcestershire sauce, a pinch of nutmeg, 3 teaspoons salt, and 1 teaspoon black pepper. Add 1 cup grated gruyère or extra cheddar in small handfuls, stirring until melted and smooth. Taste and adjust seasoning—add more salt or pepper if needed. Remove from heat and keep warm. If sauce becomes too thick, thin with 1–2 tablespoons milk.

Assemble and Bake

Layer sandwich

Place each toasted bread slice on the prepared baking sheet or keep on the skillet. Mound the warmed ham evenly over the bread slices so they are generously covered. Spoon a ladleful of the warm cheese sauce over the ham, covering it completely.

Add cheese and bake

Sprinkle the 2 cups shredded cheddar evenly over the sauced ham slices (divide roughly 1/2 cup per sandwich). Place the baking sheet or skillet in the preheated 425°F oven and bake until the cheese is bubbly and beginning to brown, 8–10 minutes. For a deeper golden crust, finish under the broiler 1–2 minutes—watch carefully to avoid burning.

Garnish and serve

Remove from oven. Sprinkle thinly sliced green onions over the hot sandwiches and add optional pickled jalapeños or banana peppers if desired. Finish with a light scattering of chopped fresh parsley. Serve immediately while hot and saucy.