Begin by preparing all vegetables: peel and cut potatoes (patatas) into uniform 1.5-inch chunks, cut carrots into similar-sized pieces, slice bell peppers (bell pepper) into ½-inch strips, and thaw the green peas (gisantes) if frozen.
Heat oil (mantika) in a large heavy-bottomed pot over medium-high heat (around 375°F/190°C). Brown the potatoes and carrots until golden (5-7 minutes), then remove and set aside. Quickly sauté bell peppers for 15-20 seconds until slightly blistered, then remove and set aside.
In the same pot over medium heat (350°F/175°C), sauté sliced onions (sibuyas) until translucent, about 2-3 minutes. Add minced garlic (dinurog na bawang) and cook until fragrant, about 30 seconds. Add chicken pieces (hiniwa-hiwang manok) and brown on all sides for 5-7 minutes.
Add the Roma tomatoes (kamatis) and cook until they soften, about 5-7 minutes. Gently mash them with a wooden spoon to release their juices. Add fish sauce (patis) and let it simmer briefly. Pour in water or chicken broth (sabaw ng manok), bring to a boil, then reduce heat to low (around 200°F/95°C). Cover and simmer for 20-25 minutes or until chicken is tender.
Return the potatoes and carrots to the pot and cook until tender, about 10-12 minutes. Add the bell peppers and green peas during the last 5 minutes of cooking. Season with salt and pepper (asin at paminta) to taste. The sauce should be rich and slightly thickened.
Serve hot with steamed white rice (mainit na kanin). For best results, let it rest for 5-10 minutes before serving to allow flavors to meld together.