Instructions

• In a large skillet over medium-high heat on the stove, warm the oil. Add the onion and cook for 3 minutes, stirring occasionally, until lightly browned. Reduce the heat to medium-low and cook another 5 minutes, stirring occasionally, or until well softened. Add the wine, thyme, ½ teaspoon salt, and ¼ teaspoon pepper and bring to a simmer. Reduce the heat, and simmer until the liquid reduces to a glaze and the onions are very tender, about 10 minutes, stirring often. Remove from the heat and cover to keep warm.
• Prepare the grill for direct cooking over medium-high heat (400° to 500°F). 
• In a medium bowl mix the ground chuck, paprika, ½ teaspoon salt, and ½ teaspoon pepper. Gently form four patties of equal size, each about ¾ inch thick. With your thumb or the back of a spoon, make a shallow indentation about 1 inch wide in the center of each patty to prevent them from doming as they cook. Refrigerate the patties until ready to grill.
• Grill the patties over direct medium-high heat, with the lid closed, until cooked to medium doneness, 9 to 11 minutes, turning once. During the last 30 seconds to 1 minute of grilling time, place a slice of cheese on each patty to melt, and toast the buns, cut side down, over direct heat. 
  Grill the patties over direct medium-high heat, with the lid closed, until cooked to well done (160°F), 9 to 11 minutes, turning once. During the last 30 seconds to 1 minute of grilling time, place a slice of cheese on each patty to melt, and toast the buns, cut side down, over medium-high heat. 
  Grill the patties over medium-high heat, with the lid closed, until cooked to well done (160°F), 9 to 11 minutes, turning once. During the last 30 seconds to 1 minute of grilling time, place a slice of cheese on each patty to melt, and toast the buns, cut side down, over medium-high heat. 
• Build each burger on a bun with a patty, caramelized onions, and baby greens. Serve right away.