Preheat oven to 350°.
Line baking sheets with parchment or Silpat.
Mix all ingredients except the flour in a large bowl, using a wooden spoon to stir after adding each ingredient. The mixture will be very wet.
Using a rubber spatula, fold in flour 1 cup at a time. Keep adding the flour until mixture becomes a dough. It should be slightly sticky but easy to work with.
Dust a workspace with flour and divide the dough into 16 pieces. Form each piece into a roll as long as your baking sheet and about 2 inches wide. Place roll onto the lined sheet, and press down to 1-inch thickness.
Bake at 350° for 20–25 minutes.
Place on wire rack to cook. Using a serrated knife, cut cooled Sesinelli crosswise into approximately ½-inch-wide slices.
For dipping, melt the chocolate in a metal bowl placed over a pot of barely simmering water, stirring until smooth. Dip each cookie halfway into the chocolate and place on a clean parchment-lined baking sheet to set. You can also use a pastry brush.
Tip: Dunk these in sweet wine like Vin Santo, or in espresso!