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1
Place the veal shoulder in the freezer for 15 minutes. Using a very sharp chef's knife, cut the cold meat into 5 mm dice — uniform, clean cubes, never ground. Set aside at room temperature while the sofregit is prepared. The texture of the finished dish depends entirely on the precision of this cut.
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2
Warm the olive oil in a wide, heavy-based pan or terracotta cazuela over medium-low heat. Add the onions and garlic. Sweat slowly, stirring occasionally, until deeply soft, translucent, and aromatic — 12 to 15 minutes. No colour should develop; the objective is collapse, not caramelisation.
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3
Add the piment d'Espelette and the diced sweet peppers. If using jambon de Bayonne, add it now. Continue to cook, covered, over low heat until the peppers are fully tender and the fat has taken on a deep red-orange hue — a further 8 to 10 minutes. The pan should smell of warm, fruity pepper throughout.
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4
Raise the heat to medium-high. Add the diced veal to the pepper base in a single layer and sear briefly — 2 to 3 minutes — stirring once or twice, until the cubes have lost their raw colour on all surfaces. This is the moment that decides the dish: if the veal is over-stirred, crowded, or left too long at this stage, the cubes will steam rather than sear and the meat will begin to break down, losing the distinct diced texture that defines axoa.
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5
Pour in the white wine and scrape any deposits from the base of the pan. Reduce the heat to low, cover tightly, and braise for 25 to 30 minutes. The veal should be tender when pressed with a spoon but hold its shape; the cubes must not fall apart. Add no stock — the veal releases sufficient juice.
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6
Remove the lid and, if necessary, raise the heat briefly to reduce the sauce to a thick, concentrated, red-orange glaze that barely covers the meat. When a spoonful of axoa holds its shape on a plate without spreading into a pool, the dish is ready. Serve from the pan or a terracotta plat creux, accompanied by riz pilaf or a thick galette de maïs.