Heat oil in a medium skillet over medium-low heat. Add the onion and a pinch of salt. Cook, stirring occasionally, until soft and golden (about 15 minutes). Set aside.
Preheat the oven to 375 degrees F. Spray the mini muffin pan with cooking spray and set aside.
Unroll the pie crusts and use a 2 1/2-inch round cutter to cut out 24 rounds (12 rounds from each crust). Fit the rounds in the cups of the muffin tin, pushing the bottoms down and pinching the sides slightly.
In a medium bowl, whisk together the half-and-half, egg and egg yolk, cayenne, and some salt and pepper until very well combined. Stir in the chives and transfer to a liquid measuring cup.
Divide the onions and ham evenly among the 24 dough-lined muffin cups. Divide the half-and-half mixture evenly among the cups.
Bake until the quiches are puffed and golden, about 20 minutes. Let the quiches cool in the muffin tin about 5 minutes, then remove to a wire rack. Serve slightly warm or at room temperature.