Preheat oven to 400 degrees F. Lightly spray two 24-count mini muffin pans with nonstick cooking spray (you will fill 36 cups total).
Thaw the puff pastry according to package directions. Lightly flour a work surface.
Unfold each thawed pastry sheet onto the floured surface. Cut each sheet into 36 equal squares (72 squares total). A pizza cutter works well for this.
Place two pastry squares in each of 36 mini muffin cups so they overlap at right angles (one square rotated 90° over the other). Gently press the squares into the cup to form a small pastry shell.
Spoon 1 tablespoon of the prepared beef brisket into each pastry cup (use 2 1/4 cups total brisket).
Sprinkle 2 teaspoons shredded cheddar (or cheddar/Monterrey combo) over the brisket in each cup (1 1/2 cups total cheese).
If using, top each filled cup with one thin slice of jalapeno (seeds removed) to taste.
Bake at 400 degrees F for 12–15 minutes, or until the pastry is golden and the cheese is melted and lightly browned.
Let the muffin pans cool for 5 minutes, then remove the bites to a cooling rack to cool slightly before serving.