Cook pasta according to directions on the box. Once cooked, drain the noodles but do not rinse. Set aside in another bowl (or keep in the colander if you used one to drain them).
Add the butter to the same pot you cooked the pasta in. Melt completely, and then add the oat flour. Mix until incorporated, and then slowly add in the oat milk. Stir with a whisk to ensure there are no clumps. Heat over medium heat until the mixture has thickened and is creamy. Lastly, turn off the burner and add the cheese. Stir until the cheese is melted. Finally, add the noodles and stir until fully incorporated.