1. Heat oil in a 5- to 6-quart pan over medium-high heat. When hot, add pork and stir frequently until browned, 2 to 3 minutes. Transfer pork to a plate. Add onion and garlic to pan; stir frequently until onion is limp, about 8 minutes.
2. Meanwhile, in a blender, whirl tomatillos and jalapeños until smooth.
3. Add 1 cup water, tomatillo mixture, pumpkin, beans, cumin, ground chilies, and salt. Reduce heat to maintain a simmer, cover, and cook, stirring occasionally, 10 minutes. Stir in pork. Cook, covered, until pork is no longer pink in the center (cut to test), 10 minutes longer. Add cilantro and lime juice.