In the bowl of a stand mixer, using the paddle attachment, combine 2 ½ cups flour, yeast, sugar, and salt.
Heat water and canola oil until warm (120°–130°F). Add to flour mixture. Add vinegar. Blend at low speed until well combined.
Switch to the dough hook and mix in the remaining flour a little at a time, to make a soft dough that’s not sticky to the touch, adding more or less flour as needed. Knead the dough for 5 minutes. Place in a greased bowl, turning to grease the top. Cover; let rise in warm place until almost double.
Preheat oven to 400º F. Grease a 9-inch springform pan, and line bottom with parchment; grease paper. Place on top of a baking sheet. Set aside.
Punch down the dough. On a floured surface, roll the dough into very thin rectangle, as thin as you can (mine was 20” x 24”). Spread a thin layer of pesto on top of the dough (leave the bottom of the long edge clear ½"). Start at the top of the long edge and slowly, tightly and gently roll the dough into a log. Pinch it closed.
Use a bench scraper to cut the dough in half lengthwise. Cross the two halves (layers facing up) to create an X shape; braid top and bottom of dough by laying the left piece over the right keeping the cut side up, until pieces of dough are tightly twisted. Pinch ends together.
Start at the thinner edge and slowly and very gently, roll the braid into a giant snail shell or a very large cinnamon bun. Be careful to keep all the layers facing up. Pinch the end delicately.
Carefully pick up the braid and place it in the prepared springform. Cover; let rise in a warm place until almost double.
Bake at 400º for 5-10 minutes, lower oven temperature to 350º and bake for an additional 20-30 minutes. When the bread is out of the oven lightly brush olive oil on top and sides. Let cool on a rack.