In a 6- to 8-quart pan over medium heat, stir pine nuts until lightly toasted, 2 to 3 minutes; pour from pan.
If using skinned chicken, pour oil into pan and turn heat to medium-high. When pan is hot, add thighs, skin side down, in a single layer (brown in batches if they don't all fit); turn occasionally until lightly browned, 10 to 12 minutes. Transfer to a plate.
Add onion to pan and stir often until limp, about 5 minutes; add chili powder and stir for about 10 seconds.
Add broth to pan and increase heat to high. Cut green chilies in half lengthwise. When broth is boiling, return chicken and any drippings to pan; add green chilies. Reduce heat, cover, and simmer for 15 minutes.
Stir rice into pan, making sure all grains are submerged. Cover and simmer, stirring occasionally, until rice is tender to bite, 20 to 25 minutes.
Uncover pan and turn heat to high; add spinach and 1/4 cup mint, pushing down into liquid, and stir gently until wilted, 1 to 2 minutes. Season to taste with salt and pepper. Ladle mixture into wide bowls, then sprinkle with remaining tablespoon mint and the toasted pine nuts.
Notes: Instead of bone-in chicken thighs, you can use 6 boned, skinned chicken breast halves (about 2 1/4 lb. total): Lightly brown them in oil as directed for skinned thighs in step 2, for 5 to 8 minutes. But instead of adding chicken in step 4, add breasts after rice has simmered for 10 minutes in step 5, pushing them down into liquid; turn over after 5 minutes and continue to cook, stirring occasionally, until rice is tender to bite and breasts are no longer pink in center of thickest part (cut to test), 5 to 8 minutes longer. Then complete step 6. Instead of the canned green chilies, you can use fresh: Rinse and dry 6 green Anaheim chilies (about 1 lb. total); lay slightly apart on a baking sheet and broil about 3 inches from heat, turning as necessary, until charred on all sides, 10 to 15 minutes total. Let stand until cool enough to touch, then pull off and discard tough skin, discard seeds, and trim and discard stem ends. Cut chilies in half lengthwise.