- Line a baking sheet with parchment paper. If baking right away, preheat the oven to 400°F.
- Combine the chopped cheddar, flour, butter and hot pepper in a food processor and pulse together until a crumbly dough forms. It should hold together when you pinch some between your fingers. If the dough is not holding together, drizzle the mixture with 1 tablespoon cold water and pulse again until it is cohesive. Transfer the dough to a bowl.
- Drain the olives and pat dry. Pinch off a small piece of dough and flatten it between your fingers to form a thin sheet. Lay an olive in the middle of the dough and wrap the dough around the olive to enclose it. Pinch off any excess dough, then roll the olive between the palms of your hand to smooth the dough. Arrange on the prepared baking sheet as you finish each olive. Repeat with the remaining olives and dough.
- If baking right away, place in the oven and bake until the pastry is puffed and golden brown, 15 to 20 minutes. Remove from the oven and serve warm.
If making ahead, place the baking sheet in the freezer and freeze until the pastry-covered olives are frozen firm, about 30 minutes. Transfer the olives to a resealable plastic bag or an airtight container and store in the freezer up to 1 month. To bake, preheat the oven to 400°F. Bake until golden brown, 20 to 25 minutes. Remove from the oven and serve warm.