To clean the morels, submerge them in a bowl of cold water, leave for 2 minutes, strain from the top, and repeat until the water that settles at the bottom is clear. Strain and pat dry with a towel. Melt the butter in a medium sauté pan over medium heat and add the shallot. Cook, stirring, until translucent, about 2 minutes. Add the morels, season with salt and pepper, and cook, stirring occasionally, for 5 minutes. Add the vermouth and reduce until almost dry. Add the chicken stock and simmer until the morels are cooked and the liquid has reduced to a glaze, about 12 minutes. Add the chicken jus and toss. Check the seasoning and set aside 12 pieces for garnish; use the rest for the crust. Reserve, chilled.