Combine flour, wine, oil, fennel seeds, and salt in a large stand mixer with a dough hook attachment. Knead on low speed. Add yeast mixture slowly. Continue to mix until a smooth ball is formed and dough pulls away from the sides of the bowl, 3 to 5 minutes.
Remove dough from the bowl; knead into a ball. Wrap in plastic wrap and let rest for 4 to 5 minutes.
Bring a large pot of water to boil over high heat.
Cut the dough into 2-inch cross sections; roll into 1/2-inch-diameter “tubes.” Cut tubes lengthwise into 1/4-inch cross sections. Roll each from the center out; fold ends over one another.
Boil taralli in the hot water in groups of 10 until they rise to the top, about 1 minute. Remove with a slotted spoon. Continue with remaining taralli. Let dry for 4 hours.
Preheat the oven to 400 degrees F (200 degrees C). Place dried taralli onto baking sheets.
Bake in the preheated oven, flipping as needed, until golden brown, 20 to 30 minutes.