Spread 1/2 tablespoon of butter evenly on the outside face of each bread slice. On the non-buttered side of one slice, spread Dijon mustard if using. Arrange the cheddar evenly on top of the mustarded slice, layering American cheese on top of cheddar if using. Season the cheese lightly with the 1/8 tsp salt and 1/16 tsp black pepper.

Cook sandwich

Heat a nonstick or cast-iron skillet over medium-low to medium heat. Place the assembled sandwich in the skillet, buttered side down. Spread the remaining 1 tablespoon of butter on the exposed top slice right after placing the sandwich in the pan. Cook gently for 3-4 minutes until the bottom is golden brown and the cheese begins to melt. Flip carefully with a spatula and cook another 2-3 minutes until the second side is golden and the cheese is fully melted. If the bread browns too quickly before the cheese melts, lower the heat and cover the pan for 1-2 minutes to trap heat and finish melting.

Remove sandwich from skillet and let rest 1 minute. Slice in half and keep warm while finishing fries or onion rings.

Fries (choice A)

Prep potatoes

Peel (optional) and cut the russet potatoes into 1/4- to 1/2-inch thick fries. Soak the cut fries in cold water for at least 15 minutes (up to 1 hour) to remove excess starch. Drain and pat completely dry with paper towels.

Fry potatoes

In a deep skillet or medium pot, heat the vegetable oil to 325°F (approximate — test by dropping one small piece of potato; it should bubble gently). Fry the potatoes in batches for 3-4 minutes until they are cooked through but not browned. Remove to a paper towel–lined tray. Increase oil temperature to 375°F. Fry the potatoes again in batches for 2-3 minutes until golden and crisp. Drain on paper towels and immediately season with 1 tsp salt and 1/4 tsp black pepper.

Serve fries hot alongside the grilled cheese with ketchup or ranch.

Onion Rings (choice B)

Prep onion

Peel the onion and slice into 1/2-inch rings. Separate into individual rings. Pat rings dry with paper towels.

Make batter and dredging stations

In a shallow bowl whisk together 3/4 cup flour, 1/4 cup cornstarch, 1/2 tsp baking powder, and 1/2 tsp salt (use part of the salt listed in ingredients). In a second bowl whisk the egg with 1/2 cup milk. Place panko breadcrumbs in a third shallow bowl seasoned with 1/4 tsp paprika if using.

Batter, coat and fry

Heat 1 cup vegetable oil in a deep skillet to 350–365°F. Working in batches, lightly dust onion rings in the flour mixture, dip into the egg-milk batter, then press into panko breadcrumbs to coat. Fry 3-4 rings at a time for 2-3 minutes, turning once, until golden and crisp. Remove to paper towels and season immediately with remaining 1/2 tsp salt. Keep warm in a low oven (200°F) while you finish remaining rings.

Serve onion rings hot alongside the grilled cheese with ketchup or ranch.

Condiments

Portion ketchup and ranch dressing into small ramekins for serving.