French Onion Burgers

Name: French Onion Burgers
Ingredients: 2 tbsp. salted butter; 2 tbsp. vegetable oil, plus more for the grill; 2 onions, halved and thinly sliced; 1/2 tsp. sugar; 1 1/2 tsp. kosher salt; 1 1/4 tsp. black pepper; 1/4 c. white wine or dry sherry; 1 tsp. fresh thyme, chopped (or 1/2 teaspoon dried); 2 garlic cloves, finely chopped; 2 lb. ground beef chuck (80% lean); 1 tbsp. Worcestershire sauce; 8 slices Swiss cheese; 2 tbsp. dijon mustard; 4 onion hamburger buns, split and toasted; 1 c. baby arugula