Vegan Pesto Babka

Stir together almond milk, yeast, and 1 tablespoon sugar in bowl of a stand mixer. Let stand until foamy, about 5 minutes. Meanwhile, stir together flour, salt, and remaining 3 tablespoons sugar in a separate bowl. Attach the dough hook attachment to mixer. Add vegetable oil to almond milk mixture; beat on low speed 5 seconds. Gradually add flour mixture, beating on low speed until dry ingredients are incorporated, about 3 minutes. Increase speed to medium; beat until dough is smooth and supple and starts to pull away from sides of bowl, 5 to 6 minutes. (Dough will be sticky.) Spray a medium bowl with cooking spray; transfer dough to bowl. Cover tightly with plastic wrap; let stand at warm room temperature until dough is doubled in size, soft, and fluffy, 40 to 50 minutes.

Place herbs, arugula, walnuts, garlic, and salt in bowl of a food processor. Pulse until finely chopped, about 10 pulses. Add olive oil and vinegar. Process until mixture resembles a coarse paste, about 10 seconds.

Turn dough out onto a lightly floured work surface; roll into a 14- x 8-inch rectangle. Spread pesto evenly over dough. Roll up dough into a tight log, starting at one long side. Using a sharp knife, cut log almost in half lengthwise, leaving 1 inch attached at one end. Twist the 2 strands of swirled dough together with cut sides facing up. 

Preheat oven to 350°F. Lightly grease a 9- x 5-inch loaf pan with cooking spray. Gently press in ends of braided dough to fit length of loaf pan; transfer to loaf pan. Cover loosely with plastic wrap. Let stand at warm room temperature until dough is doubled in size and has just risen above edges of pan, 30 to 40 minutes.

Uncover dough, and place in preheated oven. Bake until deep golden brown and an instant-read thermometer inserted in center registers 205°F, 50 to 55 minutes, tenting with aluminum foil after 30 minutes if needed to prevent excess browning. Let loaf cool in pan on a wire rack 10 minutes. Remove from pan; let cool completely on wire rack, about 1 hour, or serve warm.