Step 1Heat the broiler. Place a rack 8 inches from the heating element. Generously butter 4 (one-half cup) ramekins or 1 (2-cup) gratin dish.
Step 2Crack the crab shells into 1- to 2-inch pieces. Heat the shells, bay leaf and milk in a saucepan over low heat until the milk just starts to simmer. Remove from heat and set aside.
Step 3Cook the prosciutto in 2 tablespoons butter in a small saucepan over medium-low heat until the prosciutto softens, about 3 minutes. Add the shallots and cook until they become translucent, about 3 more minutes. Stir in the flour with a whisk. It will clump up, but don't worry.
Step 4Pour about half of the warm milk mixture through a strainer into the butter-flour mixture, whisking constantly. It will form a thick paste almost instantly. Pour the remaining milk through the strainer and whisk until smooth. Reduce the heat to low and cook until the raw taste of the flour is gone, about 15 minutes. The mixture should have the texture of a thick cream soup.
Step 5Remove from the heat and stir in the chives and one-fourth teaspoon salt. Gently stir in the crabmeat. Taste and add more salt if necessary.
Step 6In a food processor, pulse the bread crumbs, lemon zest and parsley once or twice until well combined.
Step 7Pour the crab mixture into the ramekins or gratin dish. Sprinkle with the lemon bread crumbs. Dot with 1 tablespoon butter, cut into small pieces, and broil until the gratin is bubbling and the bread crumbs have browned, about 3 to 4 minutes, checking frequently to avoid burning the crumbs. Cool briefly before serving.