Preheat oven to 375°F (190°C). Grease a 9-inch pie plate or line a muffin tin for mini quiches.
In a skillet, melt margarine over medium heat. Add chopped onions and sauté until soft and translucent, about 5 minutes. Remove from heat and let cool slightly.
In a large bowl, whisk together eggs and milk until well combined.
Add biscuit baking mix to the egg mixture and stir gently until just combined; do not overmix.
Stir in sautéed onions and shredded cheddar cheese.
Pour the batter into the prepared pie plate or evenly distribute into muffin cups, filling about 2/3 full if using mini muffin tins.
Bake for 20-25 minutes (or about 15-18 minutes for mini quiches), until the quiche is puffed, golden, and a toothpick inserted in the center comes out clean.
Let cool for a few minutes before slicing or removing from muffin tins. Serve warm or at room temperature.