Heat 2 tbsp. of vegetable oil in a large skillet over medium heat. Add onions and sauté until soft. Stir in garlic and cook until fragrant, about 30 seconds. Add the spinach and toss to evenly combine. Cook until the spinach is just wilted, about 1-2 minutes. Quickly stir in artichoke hearts and remove mixture from the heat.
Clean skillet and place over medium heat. Add the remaining olive oil.
Meanwhile, build the quesadillas. Spread 2 tbsp. of cream cheese onto a tortillas. Top with half of spinach-artichoke mixture followed by 1/2 c. of shredded cheese. Sprinkle a small pinch of red pepper flakes on top of cheese then cover with another tortillas. Repeat to make another quesadilla.
One at a time, transfer quesadillas to the pan. Cook until golden-brown, about 3 minutes. When ready to flip, cover the pan with a large plate. Invert pan to transfer the quesadilla onto the plate, then slide the quesadilla back onto the pan (golden side up). Cook until golden-brown.