Beat the butter and lemon zest with an electric mixer at medium speed until smooth, about 30 seconds. Slowly beat in the egg yolk and cream.
Whisk the flour, pecorino, 1/4 cup of the Parmesan, sugar, rosemary, salt, and nutmeg together in a bowl. Gradually add the flour mixture into the butter mixture while mixing slowly. Scrape down the sides of the bowl, then beat on medium speed to make a slightly sticky dough.
Fill the cookie press with the dough. Assemble the press with the desired disk shape (see cook's note), and press cookies onto ungreased baking sheets. Leave about one inch between cookies. Sprinkle with the remaining 1/4 cup Parmesan and refrigerate cookies for 20 minutes.
Preheat oven to 325 degrees F.
Bake cookies, rotating pan halfway through, until golden, the cheese browns a bit, and the cookies smell nutty, about 20 to 25 minutes. Briefly cool the cookies on the baking sheets, then transfer to racks to cool. Serve or store in a tightly sealed container for up to 1 month.
Cook's Notes: These freeze beautifully. Press the cookies out into desired shapes on cookie sheets and freeze. Transfer frozen cookies to a plastic bag, seal, and keep frozen for up to 1 month. When ready to bake, lay out frozen cookies on cookie trays and bake from frozen for 25 minutes.
Some disk shapes work better than others. Since this is savory cookie, we liked the cutters that result in a cracker shape cookie, like the ribbon, clover. Stars and and snowflakes work, too.
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