Instructions

for garlic confit

Combine oil and garlic in small saucepan (garlic should be just submerged. If not, add extra oil to cover). Bring to bare simmer over medium-low heat. Reduce heat to low so tiny bubbles surround garlic, but garlic is not actively frying. Continue to cook, stirring occassionally, until garlic is soft and pale tan, 30 to 35 minutes longer. (Garlic should be soft enough to smear on plate with back of spoon.)
Off heat, let garlic cool in oil for at least 15 minutes (garlic will darken slightly as it cools). Using slotted spoon, transfer garlic to airtight container. Strain oil through fine-mesh strainer into separate airtight container and reserve for another use. (Once completely cooled, refrigerate garlic for up to 1 week or freeze for up to 6 months. Refrigerate oil for up to 4 days or freeze for up to 6 months.)

for cheese coins

In small bowl, mash garlic confit with spatula or fork to form smooth paste. Process flour, Parmesan, baking powder, salt, pepper, and cayenne in food processor until combined, about 10 seconds. Add butter and garlic paste and process until dough forms ball, about 35 seconds (there may be small bits of loose dough). Transfer dough to counter and divide in half. Roll each half into 8-inch log, wrap in plastic wrap, and refrigerate until firm, at least 1 hour.
Adjust oven racks to upper-middle and lower-middle positions and heat oven to 325 degrees. Line 2 rimmed baking sheets with parchment paper. Unwrap logs and slice into ¼-inch-thick coins. Space coins ½ inch apart on prepared sheets. Bake until light golden around edges, about 16 minutes, switching and rotating sheets halfway through baking. Transfer sheets to wire racks and let coins cool completely on sheets before serving. (Coins can be stored in airtight container at room temperature for up to 1 week.)