Remove beef from refrigerator 30 minutes before cooking to reach room temperature (Hayaang uminit ang karne sa room temperature).
Heat Dutch oven over medium-high heat (350°F/175°C). Add 2 tablespoons oil. Once hot, fry potatoes (patatas) and carrots (karot) in batches until golden brown, about 3-4 minutes per side. Season with pinch of salt while hot. Remove and set aside.
In same pot, add remaining oil. When oil is shimmering, add beef in small batches (Prituhin ang karne nang pakonti-konti). Brown each batch for 3-4 minutes per side until deep golden brown (Lutuin hanggang maging golden brown). Don't overcrowd the pot. Remove browned beef to a plate.
Lower heat to medium (300°F/150°C). Add chopped onions (sibuyas) to pot. Cook until translucent and soft, stirring occasionally, about 5 minutes. Add minced garlic (bawang) and cook until fragrant, about 1 minute.
Return beef to pot. Pour in tomato sauce, tomato paste, and beef stock or water. Scrape bottom of pot with wooden spoon to release browned bits. Bring to gentle boil, then reduce heat to low (250°F/120°C).
Cover pot and simmer for 1.5 hours (Pakuluan ng dahan-dahan), stirring occasionally. Skim off any foam or excess oil that rises to surface (Alisin ang bula at langis sa ibabaw). Check tenderness of beef at 1-hour mark by piercing with fork.
Once beef is almost tender, add fried potatoes and carrots. Continue cooking for 15 minutes or until vegetables are soft but not mushy (Lutuin hanggang lumambot ang mga gulay).
Add liver spread and stir until completely dissolved into sauce. Add grated cheese in small portions, stirring until melted and fully incorporated.
Add bell peppers (pamintang pula at berde), olives, and Thai chilies (siling pangsigang). Cook for 5 minutes until peppers are crisp-tender.
Taste sauce and adjust seasoning with salt and pepper as needed (Timplahan ng asin at paminta kung kinakailangan).
Turn off heat and let rest for 15 minutes before serving. This allows sauce to thicken and flavors to meld together (Para lumapot ang sarsa at maghalo ang mga lasa).