Smashed Hamburgers with Caramelized Onions

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Canola or grapeseed oil

4 cups (1/4-inch) sliced red onions (2 medium)

1 teaspoon sugar

1 tablespoon good red wine vinegar

1 1/2 teaspoons dry mustard powder, such as Colman’s

Kosher salt and freshly ground black pepper

1 1/4 pounds ground beef with 20% fat

1 1/4 cups grated Gruyère cheese (4 ounces)

4 sandwich potato rolls, such as Martin’s

Ketchup, for serving