Sunflower Seed "Risotto" with Squash and Mushrooms

Place sunflower seeds in a medium, wide, heavy pot or Dutch oven and cover with water. Cover pot and bring to a boil, then reduce to a simmer and cook until al dente, 45–55 minutes.
Strain seeds through a fine-mesh sieve into a large bowl, reserving cooking liquid. Transfer 1 cup cooking liquid and 1 cup seeds to a blender; reserve remaining seeds and discard remaining liquid. Add cream and 2/3 cup Parmesan and blend until very smooth.
Wipe out pot. Heat 2 Tbsp. oil in pot over medium. Add onion, half of garlic, and 4 thyme sprigs. Cook, stirring, until garlic is fragrant and onion begins to turn translucent, about 4 minutes. Add reserved sunflower seeds and cook until seeds are toasted, about 1 minute. Add broth and wine and simmer over medium heat until liquid is almost fully reduced and seeds are tender, 15-20 minutes.
Meanwhile, heat 1 Tbsp. oil in a large skillet over medium-high. Add squash and cook, stirring occasionally, until just beginning to brown, 5–7 minutes. Add mushrooms, 2 thyme sprigs, and remaining garlic and 1 Tbsp. oil and continue cooking until mushrooms and squash are tender, about 5 minutes. Season with 1/2 tsp. salt and 1/4 tsp. pepper and transfer to a plate.
When broth is almost completely evaporated, add blended seed mixture and cook until sauce thickens, 5-8 minutes. Discard thyme sprigs and stir in 1 tsp. salt and 1/4 tsp. pepper; taste and adjust seasonings. Divide "risotto" among bowls and top with sautéed vegetables, Parmesan, pepper, and thyme sprigs.