Place the salt cod in a medium bowl, covering it with cold water.

Allow it to sit in the refrigerator for 24 to 36 hours, changing the water occasionally until the saltiness is reduced.

Drain the cod and then boil it in a medium saucepan filled with water.

Once boiled, transfer the cod to a plate and shred it using your fingers.

Heat 1 tablespoon of olive oil in a medium skillet over medium heat.

Add the garlic and onion, cooking until the onion becomes translucent, for about 2 to 3 minutes.

Reduce the heat to low, add the shredded cod, and cook for approximately 10 minutes.

In a small bowl, lightly beat the eggs with salt, pepper, and parsley.

Add the cooked cod mixture to the eggs and let it rest for 5 minutes.

Heat the remaining tablespoon of olive oil in the skillet over high heat until it's hot.

Quickly pour in the egg and cod mixture, ensuring an even distribution.

Reduce the heat to medium-high.

Cook, shaking the skillet often to prevent sticking, until the edges and bottom start browning, and the center is mostly set.

Carefully flip the omelet to the other side using a spatula.

Add more oil to the skillet if needed.

Continue cooking until the center is fully set but still slightly moist.