These cookies have all the flavors of gingerbread, but are softer and more textured.
Put butter, brown sugar, and 1/2 cup granulated sugar in the bowl of an electric mixer fitted with the paddle attachment. Mix on medium speed until smooth, about 3 minutes. Mix in eggs, 1 at a time, followed by the molasses and oil.
Reduce speed to low; gradually mix in flour, baking soda, cinnamon, ginger, allspice, and salt. Cover dough with plastic wrap; refrigerate until firm, about 1 hour or overnight.
Preheat oven to 325 degrees. Put remaining 1/4 cup granulated sugar in a bowl. Using a 1 3/4-inch ice cream scoop, form balls of dough. Roll balls in sugar to coat, and space 3 inches apart on baking sheets lined with parchment paper. Bake, rotating sheets halfway through, until cookies are flat and centers are set, about 17 minutes. Let cool completely on sheets on wire racks. Cookies can be stored between layers of parchment in airtight containers at room temperature up to 5 days.