For the dough: In a mixing bowl with a paddle attachment, add the dry ingredients and mix for 5 seconds to blend. Add the butter and vanilla and mix until the butter is about the size of peas. Add the cold water and blend until the dough just comes together. Form the dough into a roughly shaped ball, wrap in plastic, and refrigerate for 1 to 2 hours.
Applesauce filling: Peel, core, and slice the apples. Put the apples with the rest of the ingredients into a saucepan. Bring to a boil, turn down the heat, and cook until the apples are very soft, about 20 minutes. Remove from the heat, cool, and refrigerate.
Diced apples: Peel, core, and cut the apples into large dice. Toss with the sugar, vanilla and lemon juice and set aside.
Assemble the bomboloni: Remove the dough from the refrigerator. Roll out to 1/4-inch thick round. Cut into 6-inch rounds. Place about 1/4 cup of the Apple Sauce Filling onto the center of each round. Top with a few pieces of the Diced Apples. Pull the sides up towards the center to form a bundle, pinching the dough together towards top. Cover with plastic wrap and refrigerate for 1 hour before baking
Bake the bombolonis: Heat the oven to 350 degrees F.
Remove the bombolonis from the refrigerator and place them on a greased or parchment paper lined baking sheet. Bake until golden brown, about 25 to 30 minutes.