Caramel Cheesecake Bites

Heat oven to 350°F with rack in middle. Line a 13- by 9-inch inch baking pan with aluminum foil, leaving an overhang at both ends, and lightly butter.
Make Buttery Sugar Cookie dough as directed, but press dough evenly into bottom of pan. Use the flat bottom of a metal cup measure or a glass to compact and press the dough into as even a layer as possible.
Bake until golden, 25 to 30 minutes, then cool completely in pan on a rack, and keep oven on.
Stir dulce de leche well, then spread 1 1/4 cups of it—there will be some left over—evenly over cookie base with offset spatula and quick-chill in freezer or chill in refrigerator until cold.
Slowly beat cream cheese and sugar on medium speed with an electric mixer (fitted with paddle attachment if using a stand mixer) until creamy, about 2 minutes. Add eggs, one at a time, mixing well on medium-low speed after each addition, then mix in vanilla.
Spoon cream cheese mixture over dulce de leche. Bake until cheesecake is puffed and edges are golden, 40 to 45 minutes.
Cool completely in pan on a rack, then chill until cold, about 3 hours.
With aid of foil overhang, lift cheesecake confection from pan.
Dip a long sharp knife in a tall glass of hot water and quickly wipe it off, then trim edges of confection (save scraps for snacking). Continuing to dip knife in hot water and wiping it off before every cut, cut cheesecake lengthwise into 8 strips, then crosswise into 4 sections, to form 32 finger-shaped bites.
Just before serving, if desired, arrange bites on a large rack set over a large rimmed baking sheet, spacing them apart. Put about 2/3 cup dulce de leche in disposable pastry bag, then snip off a tiny opening. Drizzle the dulce de leche in a diagonal pattern over the bites, letting it drape down the sides.