Preheat your oven to 325°F if using the oven method and ensure your Dutch oven or heavy-bottomed pot is oven-safe. Heat the neutral oil over medium-high heat until shimmering. Add half of the beef chuck cubes and sear them, stirring occasionally, until browned on all sides, about 6 to 8 minutes. Transfer the first batch to a plate, then repeat with the remaining beef. Set all the seared beef aside.
Reduce the heat to medium. Add the quartered yellow onion and minced garlic to the same pot. Cook, stirring, until the onion is softened and aromatic, about 4 to 5 minutes. This will build a flavorful foundation for the stew.
Stir in the water, tomato sauce, soy sauce or tamari, brown sugar, bay leaves, and black pepper. Scrape up any browned bits stuck to the bottom of the pot as you stir; these add lots of flavor. I like to make sure nothing is left stuck as it really deepens the overall taste!
Return the seared beef and any juices from the plate to the pot. Stir to combine and bring the mixture to a gentle boil over medium-high heat. Once boiling, cover the pot and cook—either by transferring to the preheated oven, or by reducing the heat to maintain a low simmer on the stovetop—for 1 hour and 20 minutes to tenderize the beef.
After the initial simmer, stir in the cubed Yukon Gold potatoes and carrot chunks. Scatter the chopped red bell pepper over the top. Cover and continue to cook, either in the oven or on the stovetop, for about 1 hour, until the beef is very tender and the vegetables are soft.
Remove and discard the bay leaves. Serve the mechado hot over steamed white rice, spooning plenty of the savory sauce over everything. For a subtle lift, I sometimes garnish with a little chopped fresh parsley or squeeze a touch of lemon juice over the top.