Fried Cornmeal Shrimp with Butternut Squash Risotto

Preheat oven to 400°F. Pierce squash several times. Place on baking sheet; roast until tender, about 1 hour. Cool. Cut squash in half; discard seeds. Scoop flesh into processor. Puree until smooth. Measure 1 1/2 cups puree (reserve remaining puree for another use). DO AHEAD: Can be made 1 day ahead. Cover; chill.
Place shrimp, 1 1/2 tablespoons olive oil, and 3 smashed garlic cloves in large resealable plastic bag; turn to coat. Chill 2 to 3 hours, turning bag occasionally.
Stir cornmeal, 1/2 teaspoon salt, and 1/2 teaspoon pepper in medium bowl. Add shrimp; toss. Arrange in single layer on large plate.
Preheat oven to 200°F. Bring broth to simmer in heavy small saucepan; reduce heat to low and keep hot. Heat remaining 2 tablespoons olive oil in heavy large saucepan over medium-high heat. Add onion and cook until beginning to brown, stirring often, about 5 minutes. Add chopped garlic and 2 teaspoons thyme; stir 1 minute. Add rice and stir 1 minute. Add wine; stir until almost absorbed, about 2 minutes. Reduce heat to medium. Add 1 cup hot broth and cook until almost all liquid is absorbed, stirring often. Continue adding hot broth 1 cup at a time and stirring frequently until rice is almost tender, about 15 minutes.
Meanwhile, add enough vegetable oil to heavy large skillet to reach depth of 1/4 inch. Heat oil over high heat. Working in 2 batches, fry shrimp until golden brown and cooked through, about 1 1/2 minutes per side. Transfer to paper-towel-lined baking sheet and place in oven to keep warm.
Rewarm reserved 1 1/2 cups squash puree in microwave. Add warm puree to risotto and stir until rice is tender but still firm, about 2 minutes. Stir in Parmesan cheese and remaining 2 teaspoons thyme. Season with salt and pepper.
Divide risotto among bowls. Top with shrimp and serve.