- Place the sweetbreads in a bowl, cover them with cold water and refrigerate for about 4 hours, changing the water two to three times. Drain.
- In a saucepan, place the sweetbreads and cover with salted water. Bring to a boil. Reduce the heat and simmer for about 5 minutes. Remove from the heat, rinse under cold water and drain well. With your fingers, remove the thin membrane on the sweetbreads and break into 2.5 cm (1 inch) pieces.
- Preheat the grill, setting the burners on medium. Oil the grate.
- Thread the pieces of sweetbreads on the skewers alternately with the mushrooms, asparagus, and bell pepper pieces. Brush with butter. Season with salt and pepper. Grill the skewers for 3 to 4 minutes per side, basting with butter while cooking.
- Meanwhile, in a saucepan, soften the shallot and garlic in the butter. Add the honey and cook for 1 minute. Deglaze with the wine and reduce by half. Add the demi-glace and bring to boil. Simmer gently for about 5 minutes. Adjust the seasoning.