Put the onions, garlic, and ground beef in a large skillet. Cook until ground beef is no longer pink. Drain excess fat, then add salt and peppers. Remove to a separate bowl.
Melt butter (or margarine) in the skillet. Add flour, salt and pepper. Cook, stirring constantly over low heat for about two minutes. Do not allow to burn. Gradually add milk, stirring constantly after each addition and allowing to boil before adding more. This results in a smooth sauce. When all milk has been added, continue to stir constantly and bring to a boil. Allow to boil for one minute or until sauce is thick, continuing to stir.
Remove from heat and stir into beef mixture.
Prepare mashed potatoes: Place potatoes in a pot with enough water to cover by about 1 cm. Cook until potatoes are tender. Pour off cooking water (or save for a terrific addition to breads). Add butter (or margarine) and milk (or cream). Mash to desired consistency.
Serve ground beef mixture spooned over the mashed potatoes.
This is really good with colorful vegetables like a mixture of peas, carrots, and corn. It is a wonderful, stick-to-your ribs, warm and cozy meal. If you use low-fat beef and milk, it is a healthy meal too.
Variations: Add one teaspoon of your favorite spice blend to make a new and exciting variation. I like Adobo (Mexican), or Italian, or Jamaican. You can eliminate the cayenne pepper if you don't like spicy hot foods. If you do, then please add more!