Mince the garlic cloves and dice the onion into 1/4-inch pieces. Finely chop the fresh chives and set aside. Ensure your eggs are at room temperature, as they'll incorporate more smoothly into the cream mixture. Preheat your oven to 350°F (180°C) and spray an 8-inch (20cm) round baking dish or similar-sized pan with cooking oil to prevent sticking.
Cook the bacon until crispy in a large skillet, then remove and set aside on a paper towel. Once cooled slightly, crumble the bacon into bite-sized pieces. In the same skillet with the bacon fat remaining, add the minced garlic and diced onion, and sauté for about 2 minutes until softened and fragrant. I like using the bacon fat here because it adds a rich, savory depth that plain oil can't match.
In a medium bowl, whisk together the room temperature eggs, heavy cream, Dijon mustard, 1 tablespoon of the chopped chives, salt, and freshly ground black pepper until well combined and smooth. The whisking incorporates air into the eggs, which helps create a slightly fluffier texture in the finished quiche.
Spread about three-quarters of the bacon and onion mixture from Step 2 across the bottom of your prepared pan. Sprinkle three-quarters of the shredded cheddar cheese evenly over the bacon mixture. Carefully pour the egg custard mixture from Step 3 over the cheese layer. Top with the remaining crumbled bacon, remaining cheese, and the reserved 1/2 tablespoon of fresh chives for garnish and color.
Bake the quiche in your preheated 350°F oven for 30 to 35 minutes until the center is just set but still has a slight jiggle when you gently shake the pan. The eggs will continue to cook slightly from residual heat after removal, so it's better to err on the side of slightly underbaked rather than overbaked to keep it tender.
Remove the quiche from the oven and let it sit in the pan for 5 to 10 minutes before serving. This resting period allows the custard to set up just a bit more, making it easier to slice cleanly while still maintaining a creamy interior. Slice into wedges and serve warm or at room temperature.