Heat a large nonstick skillet over medium-high heat until hot. Add chiles; cook 2 minutes, turning frequently. Remove from heat; cool. Discard stems and seeds. Combine roasted chiles and boiling water in a bowl; cover and let stand for 20 minutes or until soft. Drain well. Combine rehydrated chiles, broth, and next 9 ingredients (broth through garlic) in a blender; process until smooth. Cook chile paste in skillet over medium-low heat until very thick (about 8 minutes), stirring frequently. Cool.

Trim fat from pork. Slice pork lengthwise, cutting to, but not through, other side. Open halves, laying flat. Place pork in a 13 x 9-inch baking dish; spread chile paste over all sides of pork. Cover and marinate in refrigerator 6 hours or overnight.

Prepare grill.

Remove pork from dish, reserving chile paste. Insert a meat thermometer into the thickest part of pork. Place pork on a grill rack coated with cooking spray; cook for 8 minutes on each side or until thermometer registers 160° (slightly pink), brushing with reserved chile paste frequently.