The landscape of butter-free cookies is usually filled with stories of compromise. Whether you're kosher and need pareve desserts, allergic to dairy, or vegan, the usual butter substitutes of margarine or shortening are rather grim; most are devoid of flavor by design. But I don't have the patience to do things without intention, and when I decided I wanted to make a butterless shortbread, I wanted it to be a shortbread that might taste even better because it celebrated its fat, rather than apologizing for it.
Growing up, I always thought rosemary tasted like pine needles and didn't understand what everyone else saw in it. A trip to Italy fixed that: rosemary crisped in olive oil and sprinkled with sea salt is now one of my favorite flavors, and I've used it to convert many a rosemary skeptic since. Chocolate and olive oil is a less popular combination, but I love the rich earthiness olive oil imparts to it. —Deb Perelman
In a large bowl, whisk together the flour, powdered sugar, 2 tablespoons turbinado sugar, and the salt. Add the olive oil and rosemary and stir to combine. Add the chocolate chunks and stir again. Gather the dough with your hands into one mass.
Roll out the dough to an 8- to 9-inch roundish slab between two sheets of parchment paper. Remove the top sheet and use the bottom to slide the cookie round onto the back of a large baking sheet.
If desired—it merely provides a little shine—brush the cookie with the egg white. Sprinkle with remaining 1 teaspoon turbinado sugar.
Bake for 20 to 25 minutes. Slide the cookie round carefully onto a cutting board while the cookie is still totally hot. Cut with a sharp, thin knife into desired shape(s). Let cool completely, then separate.
Do ahead: This dough keeps well in the freezer. Baked cookies keep for 2 weeks in an airtight tin at room temperature.
Note: For a milder flavor, replace half of the oil with a neutral/flavorless one. You can cut this into shapes with cookie cutters, too, but the chocolate provides a little resistance.