Trim excess fat from the Veal shoulder and cut into roughly 1–1.5 inch cubes; season the pieces generously with Salt and freshly ground Black pepper.
Peel and finely slice the Onions, core and cut the Green bell peppers into strips or dice, and mince the Garlic.
Heat a few tablespoons of Olive oil in a heavy Dutch oven or deep skillet over medium-high heat. In batches, brown the veal on all sides without overcrowding to develop good color, then transfer the browned pieces to a plate.
Add a little more oil if needed and reduce the heat to medium; add the onions and peppers and cook until softened and beginning to caramelize, about 8–10 minutes. Add the garlic and cook 30–60 seconds until fragrant.
Pour in the White wine to deglaze the pan, scraping up the browned bits from the bottom; let the wine reduce by about half for a minute or two.
Return the browned veal to the pot, then add enough Veal stock to come about halfway up the meat (you can add more later if needed). Season with a generous pinch of Piment d'Espelette (adjust to taste), tuck in the Bay leaf and add a few sprigs of Fresh thyme.
Bring the stew to a gentle simmer, cover partially, lower the heat and cook slowly for 1½–2 hours, or until the veal is very tender. Stir occasionally and skim any excess fat or foam from the surface.
Uncover for the last 15–20 minutes to allow the sauce to reduce and concentrate; taste and adjust seasoning with more salt and pepper if needed. Remove and discard the bay leaf and thyme stems before serving.
Serve the axoa hot spooned over mashed potatoes, polenta or with crusty bread to soak up the sauce.
