Burning Man (Smoked Ketchup Burger)

Preparation

1. Pour the carrot juice into a medium saucepan and bring to a boil. Lower the heat to a simmer, and cook till the juice is reduced to 175g (1 ¼ cups). Add the miso, paprika, liquid smoke, and vinegar. Continue cooking for 15 minutes. In a small dish, make a semi-liquid mixture with the cornstarch and a small amount of water. Add the mixture to the pot while stirring constantly. Continue to cook until the mixture thickens. Remove from the heat, and season to taste with salt and pepper. Set aside.
2. Wash and dry the arugula. Set aside.
3. Peel the yams, and shave into strips.  Place them into a bowl of ice water for an hour. Drain and dry the strips on a paper towel. Heat the oil in a deep fryer to 180°C (350°F). Fry the strips, each color separately, until firm. Remove from the oil, and place in a colander. Toss with salt, and gently mix the two different color sets of strips together.
4. Heat a skillet or grill over medium to high heat. Cook the hamburger 4 ½ minutes on each side.
5. Slice the bun in two, and slather both halves generously with the ketchup. Place the slathered bottom of the bun on a serving plate, top first with arugula, and  then the burger. Pile the yam fries on top, finish with the other half of the bun, and serve.

For the Buns

1. Put the water, sugar, and yeast in the bowl of a stand mixer, and stir until the yeast dissolves. Add the flour, puree, and salt.  Knead with a dough hook on medium speed about 10 to 15 minutes, or until the dough is smooth and elastic.
2. Place the dough in a greased bowl, cover with a towel, and let rise in a warm place until it doubles in bulk.
3. Punch down the dough, and place it on a work surface, and knead by hand for about a minute. Divide dough into buns that weigh 120g (4 oz). Roll each bun with a cupped palm to form a smooth, round bun.
4. Place the prepared buns on a baking sheet lined with parchment. Cover with a towel and let rise in a warm, draft-free place, until they double in size.
5. Heat your oven to 200°(400°F), and bake the buns for 12 minutes, or until browned. Remove from the oven, and transfer the buns to a wire rack to cool.