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1
Combine butter, olive oil, and cheese in food processor. Pulse several times, then process until well combined.
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2
Whisk flour and baking powder together in a small bowl. Transfer to food processor. Pulse for 5 or 6 one second pulses, until mixture looks crumbly.
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3
Scatter olive pieces and drizzle olive brine over the mixture. Pulse together 3 to 4 times, until no large olive pieces remain. The mixture should still be a bit crumbly in appearance, but should stick together when pressed.
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4
Transfer the dough to a sheet of waxed paper that is about 18 inches long. Form the dough into a log about 13 to 14 inches long, so it's about 1 1/4 to 1 1/2 inches in diameter. Roll up in the waxed paper. I like to form a slightly squared cylinder, but you can also leave it round.
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5
Freeze dough for 25 to 30 minutes, until it's firm but still malleable. (Or refrigerate for at least an hour.)
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6
Line a large baking sheet with parchment or silicone baking sheet. Heat oven to 350u00b0 F.
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7
Remove dough from waxed paper, and slice into 1/4-inch thick slices. Transfer slices to prepared baking sheet leaving at least 1/2-inch space between slices. (I was able to get the whole batch on one sheet, some did touch after baking but were easily separated.) Dock each cracker twice with a fork (like the dots on a domino).
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8
Bake for 20 to 22 minutes, until light golden brown and crisp. Rotate the pan 180u00b0 after 10 minutes to promote even baking. Transfer pan to cooling rack and allow crackers to cool on the pan. Once cool transfer to a sealable container. Can be made a day ahead.
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9
Combine cream cheese, parmesan/manchego, lemon zest, and pepper in a medium bowl. Whip with a hand mixer (or by hand with a wooden spoon) until creamy. Fold in the shredded radicchio by hand. (Can be made several hours ahead. Cover and refrigerate, but allow to come to room temperature before assembly.)
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10
NOTE: To shred the radicchio cut the head lengthwise into quarters, and remove the core. Cut one of the quarters lengthwise into thirds, then cut each third crosswise into thin strips. You will likely need 1 to 2 quarters, depending on the size of your raddichio. Soak the radicchio in ice cold water for 10 to 15 minutes, then drain and spin dry to temper it's bitterness.
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11
TO ASSEMBLE: Dollop about 1/2 to 1 teaspoon of cheese spread atop each cracker. Cap with a castelvetrano sliver. Serve on a pretty tray with wine, champagne, or the cocktail of your choice.
