In a 10 to 12-inch frying pan, melt butter over medium-high heat.
Add onion; stir often until limp, about 3 minutes.
Add millet and stir until it smells and tastes toasted (chew a few grains; color does not change much), about 5 minutes.
Add broth slowly; cover and simmer until millet is tender to bite and liquid is absorbed, about 20 minutes.
Stir with a fork to fluff; transfer to a serving dish.
Season to taste with salt and pepper.