Preheat the oven to 400 degrees. In a medium ovenproof skillet, heat 1 1/2 tsp. olive oil over medium-high. Add the sliced onion and cook, stirring often, until softened and lightly browned, about 5 minutes. Season with salt, then stir in the ham and thyme. Spread evenly in the skillet.
In a large bowl, whisk the eggs and season lightly with salt and pepper. Stir in the cheese; pour over the ham mixture. Bake until golden brown and just set in the center, 25 to 30 minutes. Let stand at least 5 minutes.
Meanwhile, preheat a grill or grill pan. Lightly coat the asparagus with cooking spray. Grill, turning often, until crisp-tender, 5 to 6 minutes; cut on an angle into 1-inch pieces. In a medium bowl, whisk the lemon zest and juice with the remaining 1 tbsp. olive oil; season. Add the asparagus and stir to coat. Mix in the beans, garlic and diced onion.
Cut the quiche into 6 wedges. Serve with the asparagus-cannellini salad.