Preheat oven to 400°F Line rimmed baking sheet with parchment paper. Toast cumin seeds in small skillet over medium heat until beginning to brown, about 2 minutes. Cool. Transfer to spice mill; process until finely ground. Combine parsnips, sweet potatoes, and red onion in large bowl. Add ground cumin, 2 Tb vegetable oil, chile powder, oregano, and 1 tsp coarse salt; toss to coat. Transfer to prepared baking sheet. Roast vegetables until soft and browned in spots, turning occasionally, 35 to 40 minutes cool. Do Ahead: Can be prepared 4 hours ahead. Let stand at room temperature.
Preheat oven to 375°F With machine running, add garlic and jalapeno through feed tube for processor and process until finely chopped. Add cilantro, green onions, and drained green chiles. Using on/off turns, process until coarse puree forms. Add salsa; process to blend. Transfer salsa mixture to large deep skillet. Add 1/4 cup crema and stir over medium-low heat just until warm (do not allow to boil). Remove from heat. Season salsa mixture to taste with salt and pepper. Cover and keep warm.
Measure 1 cup of roasted vegetables; set aside. Transfer remaining vegetables to processor. Using on/off turns, process until coarsely chopped. Transfer to large bowl. Add shrimp and toss to incorporate evenly. Season filling to taste with salt and pepper.
Heat remaining 3 Tb oil in medium skillet over medium-high heat. Working with 1 tortilla at a time, cook until just softened, about 15 seconds per side (do not allow to brown). Transfer tortillas to paper towels to drain.
Spread 1/2 cup salsa mixture over bottom of 15x10x2 inch glass baking dish. Place 1 tortilla on work surface; sprinkle generous 2 tsp crumbled cheese down center. Top with generous 1/4 cup roasted vegetable filling, arranging down center atop cheese. Roll up tortilla and place, seam side down, in prepared dish. Repeat with remaining tortillas, cheese, and filling. Scatter reserved 1 cup roasted vegetables over enchiladas. Spoon remaining salsa mixture over. Sprinkle with any remaining cheese; drizzle with remaining 1/4 cup crema (whisking if necessary to loosen enough to drizzle). Bake enchiladas until heated through, about 20 minutes.