Bring water, enough for peas and potatoes together, to a boil in a medium pot. Add 1/3 black-eyed peas and cook until almost tender, 15-18 minutes. Chunk potatoes and add to peas, cook for another 5-6 minutes or until potatoes and peas are both tender. Remove and drain.
In two 5" cast iron skillets* or one 10" skillet, heat olive oil over medium heat. Add in shallots and cooking until translucen, 3-5 minutes. Stir in potatoes, peas, 1 tablespoon rosemary, 2 tablespoons dill, and 1/4 teaspoon salt. Continue to cook until potatoes start to slightly brown.
Create a well in the center and add egg(s). Cover and let cook until egg is desired doneness (cook longer if you do not care for runny yolks.) Remove from heat and serve with an extra sprinkle of dill.
Notes
*If doing one skillet, divide all ingredients in half and add to each pan.