Heat a large, wide pan over medium heat. Season the chicken thighs generously with salt and pepper. Pour the olive oil into the pan and sear the chicken skin-side down first, along with the thyme and bay leaf, until golden brown and crispy.
Flip the chicken and continue cooking for another 10 to 15 minutes over lower heat. Remove the chicken from the pan and set aside with the thyme and bay leaf. Discard most of the fat, leaving about 1 tablespoon in the pan.
Finely chop the red onion and mince the garlic. Sauté both in the same pan until soft and lightly golden.
Cut 1 lemon lengthwise into quarters, remove the white pith and seeds, and cut into small pieces. Add to the pan and briefly sauté for a fresh touch.
Peel the white asparagus and remove the tough ends. Cut into bite-sized pieces. Snap or cut off the tough ends of the green asparagus and also cut into pieces.
Add the orzo, white and green asparagus, chicken broth, and mascarpone. Stir well so that the mascarpone melts nicely into the broth.
Cover the pan and let it simmer gently for about 12 minutes. Stir regularly to prevent the orzo from sticking. If necessary, add a splash of extra broth or water.
In the last minute, stir the spinach into the orzo until it has wilted. Then mix in two-thirds of the Parmesan cheese and season additionally with salt and pepper.
Cut the chicken into pieces and place on top of the creamy orzo.
Slice the second lemon thinly (without seeds) and distribute over the dish. Finish with the remaining Parmesan cheese and serve immediately.