Preheat your oven to 425°F (220°C). In a large oven-safe skillet over medium heat, melt the salted butter with the extra-virgin olive oil. Add the thinly sliced yellow onions and cook, stirring occasionally, until softened—about 5 minutes. Slowly add 1/2 cup of the dry white wine in 1/4 cup increments, letting each addition cook into the onions before adding more. Continue to cook for another 8–10 minutes, until you've used all 1/2 cup wine and the onions are deeply caramelized. I find that really taking your time with the caramelization adds loads of depth to the whole dish.
Push the caramelized onions (from Step 1) to the side of the skillet. Add your choice of lean ground turkey, chicken, or beef, along with the chopped red bell peppers (or mixed frozen vegetables), minced garlic, thyme, parsley, cayenne, and season generously with kosher salt and ground black pepper. Cook for about 5 minutes, breaking up the meat with a spatula as it cooks, until well browned. Stir in the all-purpose flour and cook for 1 more minute to eliminate the raw flour taste.
Pour the remaining 1/2 cup dry white wine, low-sodium soy sauce, Worcestershire sauce, and 1 cup of water into the skillet with the meat and vegetable mixture (from Step 2). Stir to combine and bring the mixture to a boil over medium-high heat. Once boiling, reduce the heat and let it simmer for 3–5 minutes, or until the sauce is nicely thickened. Taste and adjust seasoning as needed. Sometimes I like to add an extra splash of Worcestershire at this stage for extra umami.
Once the skillet is off the heat, evenly sprinkle the shredded Gruyère cheese over the thickened meat mixture (from Step 3). Carefully arrange the frozen tater tots in an even layer over the cheese. Transfer the skillet to the preheated oven and bake for 20 minutes, or until the tater tots are golden and crisp. Remove from the oven and sprinkle the shredded cheddar cheese evenly over the tater tots. Return to the oven and bake for 10–15 more minutes, until the cheddar is melted and bubbly.
Remove the casserole from the oven and let it cool for a few minutes before serving. Garnish with finely sliced fresh chives and extra fresh thyme if desired. For a pop of fresh flavor, I always finish with plenty of herbs on top.