Layer the onion and potatoes in a large, lined slow cooker; season with salt and pepper. Add the squash, green beans, snap peas and broth. Cover and cook until the potatoes and squash are soft and the beans and peas are crisp-tender, about 2 hours on high or 3 hours on low.
Meanwhile, make the pesto butter: Using a food processor, puree the basil and garlic until finely chopped. Add the parmesan, butter, 1/2 tsp. salt and 1/4 tsp. pepper. Process until the butter comes together in a ball. Transfer to a small bowl.
Stir the corn and tomato into the finished stew; season. Top each serving with pesto butter.