Preheat the oven to 350°F (175°C).

Boil the eggs in a small pot for about 10 minutes until hard-boiled. Peel and set aside.

In a large pot, bring 3 cups of water to a boil. Add the rice, a pinch of salt, and cook until tender, about 15 minutes. Drain any excess water and set aside.

In another pot, bring water to a boil and add the pasta. Cook according to package instructions until al dente, then drain and set aside.

Dice the onions and carrots. In a skillet, heat 2 tablespoons of olive oil over medium heat. Add the onions and carrots, sautéing until the onions are translucent and the carrots are tender.

Season the chicken breasts with salt and pepper. In the same skillet, add the chicken and cook until both sides are golden brown. This will take about 5 minutes per side. Remove from heat and slice into thin strips.

In a baking dish, spread the cooked rice evenly. Layer the sautéed vegetables over the rice. Place sliced chicken on top. Chop the boiled eggs and spread evenly over the dish.

Melt 2 tablespoons of butter in the microwave or a small saucepan. Drizzle the melted butter over the top of the rice mixture.

Peel and slice the potatoes thinly. In a separate skillet, melt the remaining 2 tablespoons of butter. Add the sliced potatoes and season with a pinch of salt and pepper. Cook until they are golden and tender.

Cover the baking dish with aluminum foil and bake in the preheated oven for 30 minutes.

Remove the foil and bake for an additional 10 minutes to allow the top to crisp slightly.

Remove the dish from the oven and let it cool for a few minutes before serving. Serve alongside the buttered potatoes.