Heat a 10-inch nonstick skillet over medium-low heat and add 2 tablespoons of the butter. Allow the butter to sizzle and become foamy, swirling the skillet to avoid burning. When you see the butter solids turn golden brown, swirl the skillet again. Keep the heat on medium-low and don’t walk away. Stir or swirl often to prevent hot spots from browning the butter unevenly. Browning the butter on medium-low heat will take 4 to 5 minutes. The foam will begin to lessen and the color will become deeper brown when it is ready.
Once the butter has browned, add the carrots. Sauté the carrots until softened, 3 to 5 minutes. Sprinkle in 1/2 teaspoon each salt and pepper and grated nutmeg to taste. Transfer the carrots to a bowl and set aside.
To the same skillet, add the remaining 2 tablespoons butter and melt over low heat. Swirl the pan to coat it all over with butter.
In a large bowl, whisk the eggs, milk, 1 teaspoon salt, and 1/2 teaspoon pepper until fully combined. Stir in the dill and 2 ounces of the cheese.
Turn the heat under the skillet to medium and pour in the egg mixture. Cover the skillet and cook the frittata for 5 to 7 minutes. Add the sautéed carrots to the center of the frittata, leaving a 1-inch edge of just egg all around. Cover and cook until the outer edges are golden brown and the center is slightly set, 5 to 8 minutes longer.
Transfer the frittata to a platter or cutting board. Top it with the remaining 2 ounces cheese, more dill, flaky sea salt, and black pepper.
Abner Ramirez and Amanda Sudano Ramirez are LA-based singer-songwriters and parents of three who love to collaborate, bond, and have fun together in the kitchen. The duo embraces the joys and challenges of cooking while juggling family life.