Preheat the oven to 450°F. Line a sheet pan with foil. Wash and dry the fresh produce. Cut the potatoes into 1-inch-wide wedges. Transfer to the sheet pan. Drizzle with olive oil and season with salt and pepper; toss to coat. Arrange in an even layer. Roast 22 to 26 minutes, or until browned and tender when pierced with a fork. Remove from the oven.

Meanwhile, halve, peel, and thinly slice the onion(s). Pick the thyme leaves off the stems. Grate the grand cru on the large side of a box grater.

In a medium nonstick pan (or large for 4 servings), heat a drizzle of olive oil on medium-high until hot. Add the sliced onion(s); season with salt and pepper. Cook, stirring occasionally, 7 to 9 minutes, or until lightly browned and softened. Add the thyme leaves. Cook, stirring occasionally, 1 to 2 minutes, or until fragrant. Add the vinegar (carefully, as the liquid may splatter). Cook, stirring constantly, 30 seconds to 1 minute, or until coated and combined. Transfer to a bowl. Taste, then season with salt and pepper if desired. Cover with foil to keep warm. Rinse and wipe out the pan.

In the same pan, heat a drizzle of olive oil on medium-high until hot. Add the patties. Cook 4 to 6 minutes, or until browned. Flip the patties and evenly top with the grated grand cru. Loosely cover the pan with foil. Cook 3 to 4 minutes, or until the cheese is melted and the patties are heated through. Transfer to a work surface.

Add the halved buns, cut side down, to the pan of reserved fond. Toast on medium-high 30 seconds to 1 minute, or until lightly browned. Transfer to a work surface. Assemble the burgers using the toasted buns, dijonnaise, cooked patties, and caramelized onion(s). Serve the burgers with the roasted potato wedges on the side. Enjoy!