Melt butter in a skillet over medium-high heat; add onion, and sauté 3 to 5 minutes or until tender.
Combine baking mix and half of cheese in a large bowl; make a well in center of mixture.
Stir together milk and egg, blending well; add to cheese mixture, stirring until moistened. Stir in onion and ham. Spoon into lightly greased muffin pans, filling two-thirds full. Sprinkle with remaining 1 cup cheese. Sprinkle with poppy seeds, if desired.
Bake at 425° for 18 minutes or until golden. Let stand 2 to 3 minutes before removing from pans.
NOTE: Substitute mini muffin pans for regular pans, if desired. Bake at 425° for 14 minutes or until golden. Makes 2 1/2 dozen mini muffins.
Reduced-fat Ham-and-Cheddar Muffins: Substitute low-fat baking mix, fat-free or low-fat shredded Cheddar cheese, and fat-free milk. Reduce butter to 1 tablespoon; proceed with recipe as directed.
Ham-and-Swiss Muffins: Substitute shredded Swiss cheese for Cheddar; whisk in 2 tablespoons Dijon mustard with milk and egg. Proceed with recipe as directed.
Sausage-and-Cheese Muffins: Substitute 1 cup hot or mild ground pork sausage, cooked and crumbled, for chopped ham. Proceed with recipe as directed.
Chicken-and-Green Chile Muffins: Substitute 1 cup finely chopped cooked chicken for ham and 2 cups shredded Mexican four-cheese blend for Cheddar; add 1 (5-ounce) can chopped green chiles. Proceed with recipe as directed.