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In a large skillet, heat olive oil over medium-high heat. Add sausage to the pan and break up the meat with a wooden spoon or a potato masher. Once the sausage is almost all the way cooked through, about 4-5 minutes, add onion and peppers, stir to combine and cook for 2-3 minutes, or until veggies are tender. Add in tomato paste and cook for about 1 minute, or until fragrant. Add in stock, stir to combine and cook another 2-3 minutes or until flavors have combined.
In a medium saucepot, heat butter over medium-high heat. Once melted, add in flour and whisk to combine. Allow the roux to cook for about 30 seconds then whisk in milk and chicken stock. Once combined, allow the sauce to heat through and come to a bubble. Once thickened, remove from heat and whisk in cheese.