Season chicken all over with salt and pepper. Heat 1 tbsp. oil in a 5- to 7-qt. pot over medium-high heat. Add half of the chicken and cook until golden brown on both sides, 4 to 5 minutes per side; transfer to a plate. Repeat with remaining chicken (if pan begins to scorch, reduce heat).
Reduce heat to medium. Add remaining tbsp. oil and onion to pot; cook until onion is translucent, 4 to 5 minutes. Add garlic and cook 1 minute, stirring constantly. Add carrots and cook just until they begin to soften, about 4 minutes. Add artichoke hearts, mushrooms, thyme, and lemon zest; stir to combine. Return chicken to pan and stir in chicken broth. Cover, lower heat to maintain a gentle simmer, and cook 10 minutes. Add asparagus, cover, and cook 6 to 8 minutes, or until asparagus is tender-crisp. Remove from heat and top with shaved parmesan.
Note: Nutritional analysis is per serving.