Preheat the oven to 280 degrees F.
Season all sides of the lamb shoulder with salt and pepper.
Heat the oil in a Dutch oven or large pot over medium-high heat and sear the lamb on both sides until golden brown, about five to six minutes per side. Remove the meat to a plate.
Lower the heat to medium-low and add the butter, shallots and garlic cloves, stirring occasionally. Cook for two to three minutes until the shallots are translucent. (Lower the heat if the shallots start to become too dark.)
Add the tomato paste and stir to combine.
Add the wine and stir to deglaze and blend the flavors together.
Add the diced tomatoes, chicken stock and bouquet garni. Return the seared meat to the pot. The lamb should be three-quarters immersed in the braising liquid. Add a bit more stock if needed.
Cover and bake for three hours.
After three hours, uncover the pot and remove the excess layer of fat if needed.
Baste with the braising liquid in the pot.
Add the potatoes, stir, cover and continue to cook for an additional hour.
Remove from the oven and let the dish rest for at least 30 minutes before serving. This will allow the meat and the potatoes to absorb all the sauce.
Finish with the zest of a lemon, freshly chopped parsley and a few pinches of Espelette pepper.
Serve with an arugula salad on the side.