Preheat oven to 475 degrees, with racks in upper and lower thirds. In a small bowl, combine paprika, 1/2 teaspoon salt, and 1/4 teaspoon pepper. Place chicken on a large rimmed baking sheet; rub with spice mixture. Roast on upper rack, basting with pan drippings once, until an instant-read thermometer inserted in thickest part of a breast (avoiding bone) registers 165 degrees, 25 to 30 minutes.
Meanwhile, mix bulgur in a medium bowl with 1 1/2 cups boiling water and 1/2 teaspoon salt. Cover; let sit until tender but still chewy, about 30 minutes. Drain in a fine-mesh sieve, pressing down on bulgur to remove liquid; return to bowl, and toss with 1 tablespoon lemon juice.
When chicken is done, transfer to a plate, and loosely tent with aluminum foil (reserve baking sheet with drippings). Place mustard greens on baking sheet, and toss with drippings; season with salt and pepper. Roast on lower rack, until wilted, about 5 minutes. Toss greens with remaining tablespoon lemon juice. Serve chicken with mustard greens and bulgur.
We rubbed chicken with a mix of paprika, salt, and pepper, roasted it on a baking sheet, then used the tasty pan drippings to season the mustard greens.