For a fancy twist on the basic bread basket, offer guests individuals bundles of dainty breadsticks.
Preheat oven to 350 degrees. Pulse flour, coarse salt, and baking powder in a food processor until combined. Add shortening; pulse until mixture resembles coarse meal. With machine running, gradually add 1/2 cup ice water; process until dough comes together. If dough is dry, add up to 1/4 cup more ice water, 1 tablespoon at a time, and pulse after each addition.
Turn out dough onto a lightly floured work surface. Pat into a rough rectangle, then roll out to an 8-by-10-inch rectangle. Cut lengthwise into 1/2-inch-wide strips.
With hands, roll each strip into a 16-inch stick; cut into four 4-inch pieces. Place on parchment-lined baking sheets. Brush with egg white. Sprinkle half with sea salt and half with Parmesan.
Bake until golden, 22 to 24 minutes. Let cool on sheets on wire racks. Bread-sticks can be stored in airtight containers at room temperature up to 3 days.