Combine chickpeas, vinegar, coriander, cayenne pepper, and cumin in a resealable bag or container with a tight-fitting lid. Store in refrigerator while prepping remainder of dish, shaking occasionally.

Bring a pot of lightly salted water to a rolling boil. Cook pasta in the boiling water till cooked through yet firm to the bite, about 8 minutes; drain and set aside.

Combine rice with enough cold water to cover; allow to soak for 20 minutes. Drain.

Meanwhile, combine lentils with enough water to cover in a pot; season with salt and pepper. Bring the lentils to a boil and simmer until tender, about 30 minutes. Drain.

Heat olive oil in a saucepan over medium-high heat; cook and stir onion and garlic in hot oil until translucent, 5 to 7 minutes. Add crushed tomatoes; season with salt and pepper, reduce heat to medium-low, and maintain at a simmer while preparing remainder of dish.

Melt butter in a pot over medium-high heat; add rice, increase heat to high, and fry for 4 to 5 minutes, stirring constantly. Pour in chicken stock and bring to a boil. Season with salt and pepper; reduce heat to low, cover, and cook until rice is tender, and the liquid has been absorbed, about 20 minutes.