Heat oven to 350°F. Line baking sheets with parchment paper. Using a
food processor, finely grind the almonds with ¼ cup flour, 1 to 2
minutes. Transfer to a large bowl and whisk in the sugar, cornstarch,
salt and remaining 2 cups flour.
In a second bowl, beat together the egg whites, oil and vanilla. Mix
the egg white mixture into the almond-flour mixture (the dough will
not hold together yet). Turn the dough onto a clean work surface and
knead 3 to 4 times to bring it together; shape into two 1-in.-thick
disks.
Roll each disk between 2 sheets of wax paper to ⅛ in. thick. Using
different-sized heart cutters, cut out cookies. With a metal spatula,
transfer the cookies to the prepared baking sheets, spacing them 1 in.
apart. Reroll and cut the scraps.
Bake, rotating the position of the pans halfway through, until the
cookies are set, 12 to 14 minutes. Let cool on the pans for 10
minutes, then transfer to a rack to cool completely. Decorate as
desired.