Broil the poblanos, turning occasionally, until the skins are blackened and blistered on all sides, 8 to 10 minutes.
While the poblanos are roasting, heat the olive oil in a large skillet over medium-high heat.
Add the onion and mushrooms and cook, stirring occasionally, until the mushrooms release their liquid and the pan looks dry again, 8 to 10 minutes.
Add the zucchini and cook until just tender, about 4 minutes.
Add the corn and garlic and cook until fragrant, about 2 minutes
When the poblanos are done broiling, transfer to a bowl, cover, and let them steam for 10 minutes.
After steaming, peel away the poblanos' charred skins and remove the stems and seeds.
Chop the poblanos.
Stir in the chopped poblanos, cumin, salt, pepper, and ½ cup of the salsa to the pan with the vegetables. Remove the skillet from the heat.
Preheat the oven to 375 F.
Wrap the stack of tortillas in foil and put it in the oven while it preheats.
Spread ½ cup of the salsa verde over the bottom of the prepared baking dish.
Spoon about ⅓ cup of the veggie filling down the center of a tortilla, roll it up, and place it seam-side down in the baking dish. Repeat the process with the remaining tortillas/filling, until the pan has a full single layer of enchiladas.
Pour the remaining salsa verde over the enchiladas, making sure the tortillas are fully coated.
Cover the dish with foil and bake for 20 minutes.
Uncover the enchiladas and top with crumbled queso fresco. Optionally top the enchiladas with chopped cilantro and green onions before serving.