In a large pot over medium-high heat, heat oil until nearly smoking. Add onion, bell pepper, garlic, oregano, cumin, allspice, red pepper, and 1 teaspoon salt. Cook, stirring occasionally and reducing heat to medium if onions get too dark, until onions are softened and golden, about 10 minutes. Add tomato paste and cook, stirring, until paste is dark red, 1 to 2 minutes.
Reduce heat to medium and add beef, breaking up into small pieces with a spoon; season with 1 teaspoon salt. Add tomatoes and cook, stirring frequently, until beef is cooked through, 5 to 7 minutes. Add wine and cook, stirring, until liquid is slightly reduced and mixture is saucy, 3 to 4 minutes.
Stir in raisins, olives, and capers and cook, stirring occasionally, until warmed through, about 5 minutes; season with remaining ½ teaspoon salt, if needed.
Divide rice among plates. Spoon picadillo over.
