Heat oil in a large skillet over medium heat. Add shallot and garlic and butter, then cook until softened. Careful to not let the mixture brown.
Add tomato paste, gochujang and red pepper flakes. Cook until paste mixture turns a deep red color, then add cream.
Add cooked pasta and parmesan cheese. Stir until cheese dissolves and water is fully incorporated into sauce. Add pasta water then stir to combine.