Preheat the oven to 450°F. On a rimmed baking sheet, drizzle potato wedges with oil and season liberally with salt and pepper. Bake 35 minutes, turning once, until very crispy.
For the horseradish sauce, combine ingredients and chill.
Heat a nonstick, flat griddle or cast-iron skillet over medium-high heat.
Combine beef with salt, pepper, grated onion and its juice, and Worcestershire. Form 4 large patties that are thinner at the center for even cooking. Grill burgers 3 minutes on each side, basting with a little steak sauce after flipping; remove to plate. Wipe grill clean and reduce heat to medium-low.
Lightly butter bread on one side.
Combine blue cheese with green onions. (If using blue jack, leave out the green onions.)
Build sandwiches with buttered sides of bread facing out: bread, cheddar, blue cheese, patty, cress, blue cheese, cheddar, bread.
Griddle sandwiches until deeply golden and crispy and the cheese is melted.