Measure the sofrito and stir it to combine any separated liquid. If using frozen sofrito, thaw it first. Check whether it already contains salt.
Crack the eggs into a bowl. Add the black pepper and, if using unsalted sofrito, the listed salt. Beat until the whites and yolks are evenly combined.
Heat the olive oil in a nonstick skillet over medium-low heat. Add the sofrito carefully and cook for approximately 3–4 minutes, stirring frequently, until fragrant and most of the loose moisture has evaporated. Do not let the garlic or herbs scorch.
While the sofrito cooks, toast the bread until lightly golden. Spread the butter evenly over the four slices and set aside briefly.
Reduce the heat to low. Pour the beaten eggs into the skillet and let them sit for approximately 10–15 seconds, until a thin layer begins to set underneath.
Using a flexible spatula, slowly sweep across the bottom of the skillet and fold the set egg toward the center. Pause briefly between folds so soft curds can form. Continue for approximately 3–5 minutes, adjusting the heat as needed.
Cook until the eggs are fully set but still tender, with no liquid egg remaining. If they begin sticking or browning, lift the skillet off the heat briefly while continuing to fold gently.
Immediately divide the eggs between two plates so they stop cooking in the hot skillet. Serve each portion with two slices of buttered toast.