Preheat oven to 425°F. Combine potato, just 1 tsp thyme, 2 tsp vegetable oil, a pinch of salt, and ¼ tsp pepper on baking sheet and toss. Roast until potato is browned and crisp in places, 18 to 22 minutes, flipping halfway through. Sprinkle with just half the cheese and continue to roast until cheese is melted, 3 to 5 minutes.

Meanwhile, heat 1 tbsp vegetable oil in same skillet over medium heat. Add onions, just ½ tsp thyme, 2 tbsp water, and a pinch of salt and cook, stirring occasionally, until deep golden brown, 17 to 22 minutes. Transfer to plate and wipe skillet clean.

Heat 2 tsp vegetable oil in same skillet over medium-high heat. Add burgers and cook until browned, 3 to 5 minutes, then flip. Top burgers with remaining cheese, cover, and cook until cheese is melted and burger is browned, 3 to 5 minutes. Transfer to plate, cover to keep warm, and wipe skillet clean.

In same skillet over medium-low heat, add butter and garlic and cook until melted. Add buns, cut side down, and toast until golden brown, 2 to 3 minutes.

Place bottom half of each bun on plates and spread with Dijon. Top each with burger and onions and close burgers with top buns. Serve with cheese fries. Dig in!

For 4-serving meal, double all ingredients. You may need to cook in batches, in larger cooking vessels, or for longer cook times. Follow visual cues in 2-serving recipe.