Make the tangzhong. Heat 3 tablespoon water with 3 tablespoon milk and 2 tablespoon bread flour in a small pot over low heat. Whisk the mixture constantly until it turns into a thick paste, about 3-4 minutes. Remove from heat and cool completely.

Meanwhile, make the sundried tomato pesto. In a food processor or blender, combine ½ cup toasted walnuts with ½ cup grated parmesan, ½ cup fresh basil, 4 ounces sundried tomatoes with 2 tablespoon of the jarred oil, 1 teaspoon minced garlic, and ¾ cup olive oil. Blend together until smooth. Season with salt and pepper and set aside.

Continue making the dough for the bread. Combine the tangzhong with 2 ½ cups bread flour, 2 tablespoon granulated sugar, 2 ¼ teaspoon instant yeast, ½ cup warm milk, 1 egg yolk, 1 egg, ¼ cup softened butter, and 1 teaspoon salt. Knead the dough until smooth about 7-8 minutes. Transfer to a clean bowl, cover, and proof in a warm area until doubled in size, about 1 hour.

Dust a clean work counter with flour and roll out the dough into a large rectangle ¼ inch thick. Spread the pesto in an even layer on the dough; you will have extra pesto leftover. Roll the dough lengthwise in a long roll. Cut the roll in half lengthwise and face the cut sides up. Braid the two ropes together to create a twist. Shape the rope into a circle and gently press the two ends together. Lightly cover the bread and proof for 45 minutes in a warm area.

Preheat oven to 350 degrees F.

Bake the sundried tomato pesto swirl bread for 25-30 minutes or until golden brown. Remove from the oven and let cool slightly. Brush on extra pesto on top and serve warm.