Preheat oven to 400°.
Sprinkle chicken with rosemary, 1/2 teaspoon salt, and black pepper. Heat the oil in a large nonstick skillet over medium-high heat. Add chicken; cook 3 minutes on each side or until lightly browned. Remove chicken from pan; cover and keep warm.
Remove casings from sausage. Add sausage to pan; cook 1 minute, stirring to crumble. Add onion and bell pepper; cook 7 minutes, stirring constantly. Add rice, tomato, paprika, saffron, and garlic; cook 1 minute, stirring constantly. Return chicken to pan. Add broth and 1/4 teaspoon salt; bring to a boil. Wrap handle of pan with foil; cover pan. Bake at 400° for 10 minutes. Stir in shrimp, asparagus, and peas. Cover and bake an additional 5 minutes or until shrimp are done.
Saffron, the exotic spice with a distinct, earthy flavor, gives this Spanish dish its characteristic yellow hue. It's a bit soupy when first prepared but quickly absorbs the liquid.