Melt butter and neutral oil in a large skillet over medium-low heat. Add sliced onions and a pinch of salt. Stir occasionally for about 30 minutes, allowing onions to turn golden-brown.

While onions are caramelizing, whisk together mayonnaise, ketchup, and relish in a small bowl until well combined and set aside.

Preheat oven according to frozen fries package instructions. Spread fries in a single layer on a baking sheet and bake for 20-25 minutes, flipping halfway through for even cooking.

Once fries are crispy, remove them from the oven and top with shredded cheese. Place back under the broiler for 3-5 minutes until cheese melts and bubbles.

After cheese has melted, spoon caramelized onions over cheesy fries, then drizzle with the special sauce. Serve immediately.