Prepare ingredients: dice the potatoes, halve the cherry tomatoes (or slice 1 large tomato), halve the red onion and separate into half sliced and half coarsely chopped, slice the cooked rotisserie chicken, and finely chop the parsley.
Heat one medium saucepan or skillet over medium heat and add 4 tablespoons of the olive oil.
Add the diced potatoes and sauté, stirring occasionally, until they are nearly cooked through and starting to brown on the outside, about 10–12 minutes.
When the potatoes are almost done, add the coarsely chopped half of the red onion and continue cooking until potatoes are fully cooked and toasted, another 2–3 minutes.
In a second medium saucepan or skillet, heat the remaining 2 tablespoons of olive oil over medium heat. When hot, cook the eggs to your liking (fried or gently scrambled), sprinkling 1/8 teaspoon salt on them while cooking; keep warm when done.
Push the cooked potatoes to one side of the first pan. In the cleared spaces, sauté the sliced half of the red onion in one area, the halved tomatoes in another, and the sliced rotisserie chicken in another, cooking each for 3–5 minutes until warmed and slightly browned.
Season the assembled potatoes, vegetables and chicken with the remaining 1/4 teaspoon salt and the 1/8 teaspoon ground pepper; stir gently to combine.
Top the chicken and potato mixture with the cooked eggs, sprinkle with chopped parsley, and serve hot.