In a large saucepan, heat oil over medium-high heat. Add the red pepper and onion; cook, stirring frequently, 4 to 5 minutes or until pepper is tender and onion is translucent. Add garlic and cook 1 minute more.
Add cheese product and milk; reduce heat to low. Continue to cook, stirring frequently, until cheese begins to melt. Stir in sriracha sauce. Continue to cook and stir until cheese is melted and ingredients are well combined, about 5 minutes.
Transfer queso to serving bowl; top with the green onions and an additional swirl of sriracha sauce, if desired. Serve with broccoli, cauliflower, and/or corn chips.