Preheat oven to 425* F. Line two cookie sheets with parchment paper. In a small bowl, mix together the cream cheese, 1/4 cup of sugar, vanilla extract, lemon zest, and a pinch of salt. Set aside.
Sprinkle about 1-2 Tbs. of granulated sugar evenly on a clean work surface. Unroll one of your sheets of puff pastry (there is usually two in a 1 lb. box). Roll it gently to seal the seams together and press some of the sugar into the dough.
Spread half of the cream cheese mixture evenly on the puff pastry. (It is important to have very softened cream cheese, or it will tear the puff pastry). Spread 2 Tbs. of strawberry jam over the cream cheese layer, adding up to 1/4 c. total depending on how much filling you want.
Starting at one end, roll the short edge of the puff pastry toward the middle a total of three times. Keep the roll tight, but do not press it too hard. Repeat on the other side, meeting the two rolls in the middle. Press them together gently. (Alternatively, you can fold the puff pastry rather than roll it. You will have a total of six folds/rolls). Repeat this whole process with the other sheet of puff pastry. Refrigerate the cookie rolls for 30 minutes, or freeze for 15.
Once the puff pastry is cold, cut the cookies into 1/4 inch slices. You will have about 16 cookies per sheet of puff pastry. Space them on the prepared cookie sheets 1-inch apart, because they will puff up significantly. Sprinkle with demerara sugar, if desired. Refrigerate any remaining cookies until you are ready to bake them.
Bake the cookies for about 8 minutes, or until the tops start to brown. Flip the cookies over, and bake for another 5-7 minutes, or until the cookies are golden brown and caramelized. Cool completely on a cooling rack before serving. Store in an airtight container for up to three days.