Prepare the Dough: In a mixing bowl, combine the sourdough discard, water, salt, honey, and olive oil. Mix until you achieve a smooth and even consistency. Gradually add the all-purpose flour, kneading the mixture for a couple of minutes until a rough dough forms. Cover the bowl with a cloth and let the dough rise at room temperature for about 1 hour, or until it has roughly doubled in size.
Preheat your oven to 400°F (200°C).
Roll Out the Dough: Dust your work surface generously with semolina. Transfer the risen dough onto the semolina-dusted surface. Roll out the dough into a rectangle about ¼ inch thick. From the short end of the rectangle, cut the dough into strips approximately ½ inch wide.
Shape the Grissini: Lightly dust the cut dough strips with semolina. Take each strip and gently roll and stretch it until it reaches a length of about 8 to 10 inches. It's perfectly fine if some end pieces are shorter. Place the shaped breadsticks on a lined baking mat, ensuring there is a ½ to 1-inch gap between each one.
Bake the Grissini: Bake the grissini in the preheated oven for about 15 minutes, or until they are golden brown. Halfway through baking, shake the baking pan gently to turn the grissini, promoting even browning on both sides.
Cool and Store: Once baked, remove the grissini from the oven and allow them to cool completely on a wire rack. Store the cooled grissini in an airtight container at room temperature. They will keep well for 2 to 3 weeks.