Arrange a rack in center of oven; preheat to 350°. Grease a baking sheet with butter.
In a large skillet over medium heat, heat oil. Cook broccoli, stirring occasionally, until bright green and tender, about 5 minutes; season with salt. Add shallots and garlic and cook, stirring occasionally, until shallots are softened, about 5 minutes. Add kale and cook, stirring frequently, until wilted, about 1 minute more. Let cool slightly.
In a medium bowl, whisk eggs, milk, cream, and Pecorino; season with salt and pepper. Pour vegetable mixture into prepared sheet.
Pour egg mixture over, making sure all corners are covered. Dollop farmers’ cheese on top. Drizzle chili crisp over.
Bake frittata until eggs are firm to touch, 15 to 17 minutes. Let cool slightly.
