Nutrition per serving may change if servings are adjusted.
1¼ cups lukewarm water
2 teaspoons sugar
1 tablespoon active dry yeast
1¾ cups whole-wheat flour, preferably white-whole wheat (see Shopping Tip)
1¾-2 cups all-purpose flour, plus more for dusting
4 tablespoons extra-virgin olive oil, divided
1½ teaspoons coarse salt, divided
Stir water and sugar in a large bowl until the sugar is dissolved. Add yeast and let stand for 10 minutes; it should bubble (if it doesn't, throw it out and start over with fresh yeast).
Add whole-wheat flour, 1¾ cups all-purpose flour, 2 tablespoons oil and 1 teaspoon salt. Mix with a wooden spoon and, eventually, your hands until combined. Add up to ¼ cup more all-purpose flour if the dough seems sticky.
Turn the dough out onto a lightly floured surface and knead until it is smooth and elastic, at least 5 minutes.
Lightly oil a clean large bowl. Gather the dough into a ball; place it in the bowl and turn to coat. Cover with a clean kitchen towel and set aside in a warm, draft-free place until doubled in size, 1 to 1½ hours.
Position racks in the upper and lower thirds of oven; preheat to 375°F. Coat 2 large baking sheets with cooking spray.
Cut the dough into 12 equal pieces. Stretch and roll each piece to about 24 inches long and approximately ⅜ inch thick. Cut each piece in half to make 2 dozen 12-inch-long breadsticks. Place about ½ inch apart on the prepared baking sheets. Brush both sides of the breadsticks with the remaining 2 tablespoons oil and sprinkle with the remaining ½ teaspoon salt.
Bake the breadsticks for 15 minutes. Gently turn each breadstick over. Continue baking until crisp and golden brown, 15 to 20 minutes more.
Make Ahead Tip: Tightly wrap cooled breadsticks in plastic wrap and keep for up to 5 days.
Shopping tip: White whole-wheat flour, made from a special variety of white wheat, is light in color and flavor but has the same nutritional properties as regular whole-wheat flour. Find it in large supermarkets or online from kingarthurflour.com.
Easy cleanup: Recipes that require cooking spray can leave behind a sticky residue that can be hard to clean. To save time and keep your baking sheet looking fresh, line it with a layer of foil before you apply the cooking spray.