In a large Dutch oven over medium-high heat, heat 1 tbs oil. Brown the chicken on all sides, 5 to 7 minutes. Remove from pan and set aside.
Sprinkle the flour, mustard, paprika, red pepper flakes, and pinch of salt and pepper over top and cook for 1 minute, stirring the whole time.
Carefully, whisk in a bit of the milk. The flour will quickly absorb it. Whisk in the remaining milk slowly so that no lumps form. When smooth, whisk in the broth, in a slow steady stream.