Bring a large pot of water to boil over high heat. Add tomatillos, summer squash, onion, garlic, and jalapeños.
Boil vegetables for 8-10 minutes, stirring occasionally, until tomatillos are starting to split and vegetables are very soft.
Transfer to a blender along with cilantro, salt, and zest plus juice of lime. Blend until smooth.
Preheat oven to 350º. Heat canola in a Dutch oven or large skillet (with lid) over medium heat.
Season pork generously on both sides with salt and pepper. Working in batches as needed, add pork to skillet and sear on top and bottom, about 3-4 minutes per side. Remove to a plate with a slotted spoon.
Add mushrooms to the pot and cook, stirring occasionally, until shrunken and starting to brown, about 7-10 minutes.
Add salsa verde and pork to the pot, mix to combine. Transfer to oven and braise for about 2-2½ hours, stirring after 1 hour and then every 30 minutes after that. When pork is done it should fork tender.
Serve chile verde with rice, beans, and tortillas, as desired.