In a food processor fitted with a steel blade, process the sugar for about 15 seconds to a fine powder. Add the flour, cornstarch, baking powder, and salt and run the motor for 15 seconds until well incorporated.
Evenly scatter the cream cheese and butter cubes over the flour mixture, breaking up any pieces that have clumped together. Combine the dough with 15 one-second on/off pulses until the flour looks like coarse meal.
In a small bowl beat the vanilla and the yolks. Pour them over the flour. Pulse with 10 one-second on/off turns, scrape down the sides, then process with the motor continuously running for about ten more seconds until the dough barely starts to come together and clings to the outer portion of the bowl, leaving the center clear. The dough will be dry and crumbly.
Turn the dough out onto a lightly floured surface and push it together with your hands to form a ball. Do not knead. Divide the dough into thirds, pat each into a flat 5-inch disk, and wrap in plastic. Refrigerate for 30 minutes.
Take one disk out of the refrigerator and roll it out between two sheets of lightly floured waxed paper to a long oval shape 1/8 inch thick. If the dough sticks to the paper and is difficult to roll out, remove the waxed paper from one side, lightly flour the dough, replace the waxed paper, flip over, lightly flour the other side, then continue rolling. Roll out the other disks in the same manner. Place the dough ovals in the refrigerator for at least 30 minutes, or up to 2 days, or in the freezer for three months. When you are ready to bake the alfajores, position the racks in the top third and bottom third of the oven and heat to 375°F (190°C). For best results, line ungreased baking sheets with parchment paper.
Take one sheet of dough out of the refrigerator at a time, remove the waxed paper from one side of the dough, lightly flour it, and replace the waxed paper. Flip it over, peel off the other sheet, and cut the dough into as many 2-inch (5-cm) rounds as possible, reserving the scraps. Place the cookies on the baking sheets about 1/2 inch apart. Continue with the remaining dough in the same manner. Combine all the scraps once and repeat the same steps for rolling, cutting, and baking.
Bake the cookies for 12 minutes, rotating the baking sheets halfway through baking time from front to back and top to bottom until the cookies have a golden edge and bottom. Let the cookies rest for 2 minutes on the baking sheet and then cool on wire racks. The cookies can be stored in an airtight plastic container at room temperature for 2 days or in the freezer for 3 months.