In a skillet, heat olive oil and melt butter and add onions and thyme. Saute (keep stirring) until caramelized. This takes 15-20 minutes. Remove the thyme sprigs, season with salt and pepper, and remove from heat.
Lightly butter a 7x11” pan with softened butter, and preheat the oven to 350°F/180°C.
Slice the rolls lengthwise leaving them intact, and place the bottom half in the buttered pan. Spread the mayo and mustard
Then add a layer of cheese (use half of the cheese), all of the roast beef, and the caramelized onions. Layer the remaining cheese, and cover with the top buns over the cheese.
Brush the buns with melted butter, and sprinkle with dried onion mix. Bake in the oven covered with foil for 15 minutes, then uncover and bake for 5 more minutes or until the tops are golden brown.
Prepare the au jus gravy as you wait for the sliders to bake, and serve on the side. Garnish with parsley.