Preheat the oven to 400℉. Line a baking sheet with parchment paper and set aside. Peel the pumpkin and cut into a small dice. Toss with 2 tbsp olive oil and a sprinkle of kosher salt and pepper. Spread the pumpkin out on the baking sheet and roast for 30 to 40 minutes or until tender. Flip the pumpkin halfway through to encourage even browning.
In a wide skillet, heat the butter and olive oil over medium heat until the butter begins to melt. Add the sliced onion along with the kosher salt. Cook for 3 to 4 minutes over medium heat until the onions begin to soften. Turn the heat down to low and cook until the onions are well browned and softened.
Add the minced garlic, chopped thyme, and pepper. Sauté for 1 minutes then remove from the heat. Add to the roasted pumpkin. Allow the mixture to cool completely before adding the shredded cheese. Chill until ready to assemble.