IN a large mixing bowl, toss Yukon Gold potatoes, parsnip, turnip, and sweet potato with the ½ teaspoon salt. In a large nonstick skillet, heat the olive oil over medium high heat until shimmering.
REDUCE heat to medium low and add the vegetables in an even layer. Cook until vegetables are halfway cooked, about 7 minutes, stirring occasionally to prevent sticking and browning.
ADD the onion, reduce heat to low, and cook until everything is soft, about 15 minutes more. Transfer the vegetables to a colander set over a bowl using a slotted spoon and drain thoroughly. Remove 3 tablespoons of the cooking oil; strain the remaining oil and save for another use (It is deliciously flavored from the onion).
BEAT the eggs, chicken broth, and a pinch of salt in a large bowl. Gently fold in the vegetable mixture and lightly mash the vegetables with a fork to crush them into the eggs. Return the skillet to the burner and heat 2 tablespoons of the reserved oil over medium high.
POUR the egg mixture into the pan and flatten the vegetables with a spatula until the top is even. Reduce heat to medium-low and cook. Cover and cook for 10 minutes, sliding a spatula underneath the eggs to prevent sticking as the eggs begin to set.
WHEN the top of the tortilla is moist, but not overly wet, loosen it from the skillet with a spatula, then place a large plate on top of the skillet, serving side down, and quickly invert the pan to release the tortilla from the skillet.
RETURN the skillet to the burner. Add the remaining 1 tablespoon reserved oil, then slide the tortilla back into the skillet; use the spatula to reshape the tortilla if needed. Reduce heat to low. Cover and cook until the tortilla is set and a toothpick comes out clean when inserted into the center, about 5 minutes.
SLIDE the tortilla on the plate again and pat the surface dry with paper towels. Slice into wedges and serve with green romesco.