In a food processor or bowl, combine 1 1/2 cups flour (1 1/4 cups if using Cornmeal-Parmesan Seasoning Mix), seasoning mix, and salt; whirl or stir to blend. Add butter and pulse or cut in with a pastry blender until mixture forms 1/4-inch crumbs.
Sprinkle 3 tablespoons cold water (or lemon juice, if using Lemon-Anise Seasoning Mix) over mixture and pulse or mix with a fork until evenly moistened. Gently squeeze about 1/4 cup of the dough into a ball; if it won't hold together, crumble lump back into bowl, sprinkle with 1 to 2 more tablespoons cold water, and pulse or mix again until dough is evenly moistened and holds together.
With lightly floured hands, press dough into a ball; dust lightly with flour and press into a 1/2-inch-thick rectangle (4 1/2 by 6 1/2 in.). Press edges to make smooth.
On a lightly floured board, with a lightly floured rolling pin, roll dough firmly but gently in short strokes from the center outward into a 1/8-inch-thick rectangle (10 by 12 in.). Trim edges to make even. Sprinkle sesame seeds (or coarse sugar, if using Lemon-Anise Seasoning Mix) evenly over dough and roll lightly into surface without enlarging rectangle.
With a fluted pastry wheel or a knife, cut rectangle in half crosswise, then cut lengthwise across whole rectangle into 1/2-inch-wide strips. Brush lightly with beaten egg; save remaining egg for other uses or discard. One at a time, lift strips by both ends and transfer to 12- by 15-inch baking sheets (you'll need two), spacing about 1 inch apart.
Bake savory straws in a 375° regular or convection oven (sweet ones at 350°) until lightly browned and crisp, 12 to 20 minutes. Cool on sheets 1 minute, then transfer to racks with a wide spatula. Serve warm or cool.
Classic Cheddar Seasoning Mix: In a small bowl, mix 3/4 cup shredded sharp cheddar cheese and 1/4 teaspoon cayenne.
Per straw: 42 cal., 57% (24 cal.) from fat; 0 g protein; 7 g fat (6 g sat.); 4 g carbo (1 g fiber); 56 mg sodium; 11 mg chol.
Curry Seasoning Mix: In a small bowl, mix 2 teaspoons curry powder and 1/4 teaspoon cayenne.
Per straw: 36 cal., 53% (19 cal.) from fat; 6 g protein; 1 g fat (2 g sat.); 5 g carbo (2 g fiber); 45 mg sodium; 8 mg chol.
Cornmeal-Parmesan Seasoning Mix: In a small bowl, mix 1/2 cup grated parmesan cheese, 1/4 cup yellow cornmeal, and 2 teaspoons Italian seasoning (or 1 teaspoon each dried basil and dried oregano).
Per straw: 40 cal., 55% (22 cal.) from fat; 9 g protein; 4 g fat (4 g sat.); 5 g carbo (1 g fiber); 61 mg sodium; 4 mg chol.
Lemon-Anise Seasoning Mix: In a small bowl, mix 1/3 cup granulated sugar, 2 teaspoons grated lemon peel, and 1 1/2 teaspoons anise seeds.
Per straw: 41 cal., 44% (18 cal.) from fat; 6 g protein; 2 g fat (2 g sat.); 1 g carbo (1 g fiber); 45 mg sodium; 8 mg chol.