Preheat the oven to 375 degrees F. Grease a standard muffin pan and set aside.
In a small skillet, melt the 1 tablespoon butter over medium heat (if you used a skillet to cook the bacon, then you can use bacon drippings!). Add the onion and sauté until soft and browned, about 5 minutes. Remove from the pan to cool.
In a large bowl, whisk together the flour, baking powder and salt. Using a pastry cutter, cut the butter into the flour mixture until combined and the mixture is crumbly.
In a small bowl, whisk together the milk, oil and egg.
Add the milk mixture to the dry ingredients, and gently toss with a fork until the flour mixture is mostly moistened (lumps will remain). Add the bacon, onions and cheddar cheese. Using a rubber spatula, gently mix together until combined.
Spoon the batter into the prepared muffin pan. Bake for 20 to 22 minutes, or until golden brown. Allow to cool for 10 minutes, then remove from the pan and serve warm or at room temperature. The biscuits are best the day they are made, but can be stored in an airtight container at room temperature for up to 2 days.
Notes
You can substitute 1 tablespoon of bacon drippings for the 1 tablespoon of butter used to cook the onions.
You can skip the muffin tin and just scoop the biscuit dough onto a parchment-lined baking sheet for drop biscuits.