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Pat the chicken legs and beef chuck pieces completely dry with paper towels, then season generously all over with salt. Heat 4 tablespoons of olive oil in a large, heavy-bottomed Dutch oven over medium-high heat until shimmering. Working in uncrowded batches, sear the meat on all sides for 4–5 minutes per side, allowing each piece to develop a deeply caramelised, mahogany crust before turning — resist the urge to move them early. Transfer the browned pieces to a plate and repeat with remaining meat, 8–10 minutes per batch.
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Reduce the heat to medium and add the remaining 2 tablespoons of olive oil to the same pot. Add the diced onions and cook, stirring occasionally, for 5–6 minutes until completely softened, fragrant, and just beginning to colour at the edges — they should look almost jammy and translucent. Add the minced garlic and stir for a further minute until deeply aromatic and the raw edge has disappeared.
2
Add the tomato paste and stir vigorously to coat the onions and garlic, pressing it against the bottom of the pot. Cook for 1–2 minutes, stirring constantly, until the paste deepens to a brick-red and releases a rich, concentrated sweetness — it should smell intensely of caramelised tomato rather than raw tin.
3
Pour in the red wine and use a wooden spoon to scrape up every golden-brown bit stuck to the bottom of the pot — those caramelised fragments are the soul of the braise. Simmer briskly for 2–3 minutes until the sharp alcohol edge softens and the liquid reduces slightly. Add the beef stock, fresh tomatoes, chopped thyme, paprika, and dried oregano, stirring to combine everything into a cohesive, fragrant base.
4
Nestle the browned chicken and beef back into the pot, pushing them down so they sit comfortably in the liquid. Bring to a gentle simmer, then reduce the heat to low and partially cover with a lid — a slightly ajar lid encourages slow evaporation and a beautifully concentrated braise. Cook for 45–50 minutes, stirring occasionally, until the meat yields easily when pressed with a fork and the liquid has thickened and turned deeply savoury.
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Stir in the cooked kidney beans, pink beans, and kale, folding them gently through the braise. Season assertively with salt — beans and greens absorb seasoning quickly and the dish can taste flat without adjustment at this stage. Simmer uncovered for a further 15–20 minutes until the beans are warmed through, the kale is tender and silky, and the whole pot smells unified and deeply aromatic.
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Just before serving, squeeze fresh lemon juice over the braise and stir gently — the acidity should lift and brighten the rich, wine-dark flavours without announcing itself. Taste for final seasoning, ladle into wide shallow bowls, and finish with a drizzle of your best fruity olive oil. Bring the pot straight to the table and serve family-style with plenty of crusty bread for sweeping through the braise.