In a small saucepan, bring 3 cups water to a rolling boil over medium-high heat; reduce heat to a simmer. Add 1 cup raw cashews (about 4.5 oz.) and cook until softened, about 20 minutes.

Drain cashews (discard cooking liquid) and rinse well. Transfer cashews to a blender, add 2 Tbsp. lemon juice, ½ tsp. Diamond Crystal or ¼ tsp. plus ⅛ tsp. Morton kosher salt, and 1½ cups water, and purée on high until completely smooth and creamy, about 1 minute. Transfer to a medium bowl; set aside. Do not rinse blender. (Makes about 2¼ cups cashew crema.)

Heat 2 Tbsp. extra-virgin olive oil in a stockpot or Dutch oven over medium. Add 2 small onions, diced (about 2 cups) and 2 garlic cloves, coarsely chopped and cook until soft, about 5 minutes. Add 1 medium zucchini (about 8 oz.), peeled, chopped, 3 jalapeños, stemmed, halved lengthwise, seeded, and 1 cup fresh or frozen corn kernels (about 5 oz.); cook until vegetables start to brown around edges, 10–15 minutes. Using tongs, remove jalapeños to a cutting board and reserve.

Add all but 3 of 8 oz. squash blossoms (about 30), stemmed, stamens removed to the pot and cook until just starting to wilt, about 45 seconds. Transfer vegetables to reserved blender, add 1¼ cups low-sodium vegetable or chicken broth and half of reserved cashew crema, and purée on high until smooth, about 1 minute.

Pour soup back into pot and bring to a simmer over medium-low heat. Season with remaining 1 tsp. Diamond Crystal or ½ tsp. plus ⅛ tsp. Morton kosher salt and remove from heat. Taste and stir in more cashew crema if needed; reserve the rest for serving.

Thinly slice reserved jalapeños and cut remaining 3 squash blossoms in half; scatter both over soup. Top with freshly ground black pepper and serve with remaining cashew crema for drizzling.