Adapted from Ina Garten's recipe in Barefoot Contessa Back to Basics
and from the view from great island
Place the flour, cheese, rosemary, salt and pepper into the bowl of a food processor. Add the chunks of soft butter and pulse about 30 times to combine into a crumbly mixture. The process of pulling the dough together should not take longer than 30 seconds to a minute. If the dough does not come together in that time, add a tiny bit of water to the bowl, start with 1/2 tsp, and process again. If making gluten-free, the flour mixture will likely require additional water.
Turn the dough out onto a piece of plastic wrap and bring it together into a smooth flat disk, just like you do with pie crust dough. The dough should be smooth and uniform, without dry floury parts. Knead it with your hands if necessary. Wrap the disk in the plastic and refrigerate for at least an hour.
Preheat the oven to 350°F. Position the oven rack in the middle.
Roll out the dough to about 1/4-inch thickness. The dough is rolled out between two sheets of waxed paper which prevents the dough from sticking to the rolling pin.
Once the dough is rolled out evenly to a 1/4-inch thickness, take your 2-inch round cookie cutter and press lightly all over the surface so that you have a guide as to where to place the fresh herb sprigs. Once you have them situated, put the waxed paper back over the top and give it all one more light pass with the rolling pin. The herbs will then be embossed right into the dough.
Following the embossed spheres as a guide, use a 2-inch round cookie cutter to cut out your circles. Carefully transfer each round onto a baking sheet. Gather up the leftover dough, roll and repeat until all of the dough is used.
Bake the shortbread crackers for 13-15 minutes, until they are just starting to turn pale golden around the edges. Cool for a few minutes on the pan, then gently transfer them to a cooling rack. The shortbread will firm up considerably as it cools.
Make Ahead: You can make the crackers up to a couple of days ahead of time. Or prepare and freeze the dough until ready to use.
Keep in mind that depending on the moisture content of your butter and cheese, you may need to add a tiny bit of water to your dough to bring it together. Also, if using gluten-free flour, you will most likely need additional water. Start with 1/2 teaspoon and go from there.