Let puff pastry thaw for about 40 minutes, until easy to handle and roll out. If using refrigerated pastry, keep it chilled until ready to use.
Meanwhile, combine strawberries, jalapeno, and sugar in a small saucepan over medium heat.
Cook, stirring often, until strawberries have broken down and the mixture is thick and jammy — about 15 minutes. Remove from heat and let cool.
Roll puff pastry out to an approximate 8-by-12-inch rectangle. Spread the jam in a thin layer on the pastry. Don't use too much, as it will leak out when you slice the pastry. (If you have extra, save it for putting on toast.)
Starting from one long end, roll up the pastry halfway. Roll the other long end to meet it. Place the rolled pastry on a lined baking sheet and put in the refrigerator to chill. Meanwhile, preheat the oven to 400°F and line a baking sheet with parchment paper.
Slice dough into 1/4-inch pieces and place onto prepared baking sheet. Don't worry if it looks a little misshapen, because they will form properly in the oven (although you can adjust before baking if you like).
Bake 15-20 minutes, until golden brown. Let cool completely on a wire rack.
Frozen puff pastry can be thawed in the refrigerator overnight.
If you like, sprinkle on sparkling sugar before baking for added sweetness and crunch.