How to Make It
Heat 1 tablespoon of the oil in a medium saucepan over medium. Add mushrooms, and cook, stirring occasionally, until tender and browned, 6 to 7 minutes. Add flour and 1 tablespoon of the oil, and cook, stirring constantly, until flour is slightly toasted, about 20 seconds. Add garlic, turmeric, and paprika; cook, stirring constantly, until fragrant, about 30 seconds. Gradually add 3 cups of the broth, whisking constantly. Increase heat to medium-high, and bring to a boil.
Reduce heat to medium to maintain a simmer. Stir in oyster sauce, sesame oil, and 1 tablespoon of the soy sauce. Simmer until slightly thickened, about 4 minutes.
Stir together 1/4 cup of the cornstarch and remaining 1/2 cup broth in a medium bowl. Slowly drizzle cornstarch mixture into simmering sauce, and simmer until sauce coats the back of a spoon, about 1 minute. Cover and keep warm.
Toss shrimp with 1 teaspoon each of the cornstarch and soy sauce. Heat 1 tablespoon of the oil in a large wok or skillet. Add shrimp, and cook, stirring occasionally, until opaque, 3 to 4 minutes. Transfer shrimp to a large bowl, and cool 5 minutes.
While shrimp cool, heat remaining 2 cups oil in a large cast-iron skillet or wok over medium-high to 350°F.
Add sprouts, onion, eggs, scallions, and remaining 1 tablespoon cornstarch and 1 teaspoon soy sauce to shrimp. Fold mixture gently just until eggs are lightly beaten. (Do not overmix, or patties will become too watery and fall apart.)
Scoop shrimp mixture in 1/3-cupfuls into hot oil; fry until golden, about 2 minutes per side. Transfer patties to a plate lined with paper towels to drain. Sprinkle patties with pepper, and garnish with scallions. Serve hot with rice and mushroom gravy.