If making on the same day, preheat oven to 425°F. Heat oil in a Dutch oven over medium heat. Add onion and garlic and cook, stirring occasionally, until lightly browned, approx. 5-8 minutes.
Add spinach and kale in two additions, letting the first batch wilt down before adding the next. Add corn and cook until greens are completely wilted, tossing frequently, approx. 6-8 minutes. To remove all excess liquid, transfer to a colander and drain. (If you are making this in advance, simply allow the spinach and kale mixture to cook before transferring to an airtight container and refrigerate.)
Bring milk to a simmer. Add cream cheese and cook, whisking, until melted and well incorporated. Add the spinach and kale mixture, Worcestershire sauce, sriracha, and ¼ cup mozzarella. Stir to combine. Season with salt and pepper. Transfer mixture to a lightly oiled shallow baking dish. Top with remaining ¼ cup mozzarella. Bake until cheese is golden brown and bubbly, about 20-25 minutes. Serve hot.