Add asparagus pieces to a microwave-safe bowl or plate. Cook for 3-4 minutes to soften a bit. I like to soften the asparagus briefly in the microwave so it becomes very tender once cooked with the chicken.
Season chicken with salt and pepper on both sides. Melt 1 tablespoon butter and 1 tablespoon olive oil together in a large, nonstick pan/skillet over medium-high heat. Stir in garlic and herbs and cook another minute until the garlic is fragrant. Reduce heat to medium, add chicken to pan, and cook for 5 minutes, then flip and cook another 5-7 minutes. (Chicken should be almost done but not completely through by this point).
Move the chicken thighs over to the sides and add the remaining 1 tablespoon butter and 1 teaspoon olive oil to the middle of the pan. When the butter is melted, add softened asparagus. Season asparagus with salt or garlic salt and pepper, to taste. Squeeze the juice of ½ lemon all over the top. Continue to cook asparagus, rotating throughout, for 4-6 minutes until very tender and chicken is completely cooked through.
Remove chicken and asparagus to a serving plate. Scrape the bottom and sides of the pan and drizzle the liquid over the chicken.
Any leftovers freeze great.