In a large pot or deep skillet, heat the olive oil over medium-high heat. Add the chicken legs and sear until the skin is golden brown on all sides.
Add the diced onion, carrots, celery, and the knob of butter to the pot. Sauté until the vegetables soften and become aromatic.
Stir in the tomato paste and sauté for about a minute to caramelize it. Season generously with salt and pepper, then pour in 1 cup of water.
Cover the pot with a lid and reduce the heat to low. Let it simmer gently for 30 minutes.
Add the cubed potatoes and peas to the pot. Stir gently to coat them in the sauce. Cover again and cook for another 30 minutes, or until the potatoes are fork-tender and the chicken is falling off the bone.
Remove from heat and top with fresh basil leaves.
