- 2 medium sweet potatoes, peeled and cut into 1-inch pieces
- 2 medium carrots, peeled and cut into 1-1/2-inch pieces
- 2 medium zucchini, cut into 1-1/2-inch pieces
- 3 Tbs. olive oil
- 1 Tbs. unsalted butter
- 1 Tbs. finely chopped fresh sage
- 1/4 tsp. cayenne; more to taste
- Kosher salt
- 8 large eggs, at room temperature
- Freshly ground pepper
- 4 oz. smoked Cheddar, coarsely grated (about 1-1/2 cups)
Position a rack 6 inches from the broiler and heat the broiler on high.
Working in two batches, pulse the sweet potatoes, carrots, and zucchini in a food processor until chopped, with pieces no larger than almonds in the mix. Transfer to a bowl.
Heat the oil and butter in a 12-inch cast-iron skillet over medium-high heat until the butter melts and the foam subsides. Add the vegetables and the sage and cook, stirring often, until tender and golden-brown in spots, about 10 minutes. Remove from the heat and season with the cayenne and 1-1/2 tsp. salt.
Smooth the surface of the hash and crack the eggs over it, leaving a little space between each egg. Season each egg with salt and pepper and broil until the whites are set, 1 to 2 minutes. Sprinkle the Cheddar evenly over the eggs and hash and broil until the cheese is melted, about 1 minute.
Let cool slightly before serving.
nutrition information (per serving):
Calories (kcal): 310; Fat (g): 22; Fat Calories (kcal): 190; Saturated Fat (g): 8; Protein (g): 15; Monounsaturated Fat (g): 10; Carbohydrates (g): 14; Polyunsaturated Fat (g): 2.5; Sodium (mg): 530; Cholesterol (mg): 275; Fiber (g): 3.