Place cubed jicama in a large microwave safe bowl with ¼ cup water. Cover with plastic wrap and microwave for 25 minutes. Drain well and set aside. Pat dry.
In a large skillet, brown the chorizo and set aside.
In a large skillet, heat the olive oil for medium-high heat. Brown the jicama in the pan.
Add the onion, ¼ cup water, and salt and pepper. Sauté until soft, about 3 minutes. Stir in cooked chorizo and bell pepper.
Make 6 wells in the mixture and crack an egg into each well. Cover and let cook until the eggs are cooked to desired consistency.
Top with feta and cilantro if desired.