Warm the olive oil in a large, deep skillet over medium heat until shimmering, 1–2 minutes.
Add the yellow onion (finely chopped) and green bell pepper (finely chopped); cook, stirring, until softened and lightly golden, 6–8 minutes.
Stir in the garlic (minced) and cook until fragrant, about 30 seconds.
Add the ground beef; sprinkle with the kosher salt and ground black pepper. Cook, breaking the meat into small crumbles, until no longer pink and lightly browned, 6–8 minutes; spoon off excess fat if needed.
Sprinkle in the ground cumin and dried oregano; stir and cook to bloom the spices, about 30 seconds.
Add the tomato paste and cook, stirring, until it darkens slightly and coats the meat, about 1 minute.
Pour in the dry white wine, scraping up any browned bits; simmer until reduced by about half, 2–3 minutes.
Stir in the tomato sauce, bay leaves, pitted Spanish green olives (sliced), raisins, and capers (rinsed). If the mixture looks dry, stir in the water. Bring to a gentle simmer.
Reduce heat to medium-low and simmer uncovered, stirring occasionally, until the sauce is thick and glossy and the flavors are well combined, 15–20 minutes; it should hold a shallow trail when a spoon is dragged through.
Remove the bay leaves and let the picadillo rest off heat for 5 minutes.