Shiitake and Chanterelle Pizzas with Goat Cheese

1. For dough: combine all flours, coarse salt, and sugar in processor. Stir 1 cup plus 2 tablespoons warm water and yeast in 2-cup measuring cup. Let stand until yeast dissolves, about 5 minutes.
2. Stir in 3 tablespoons oil. With machine running, pour yeast-oil mixture through feed tube. Blend until ball of slightly sticky dough forms, about 1 minute.
3. Transfer dough to lightly floured surface; knead until smooth and elastic, adding more flour if very sticky, about 5 minutes. Rub with 1/2 tablespoon oil; place in resealable 1-gallon plastic bag. Seal bag. Let dough rise at room temperature until doubled, about 2 hours.
4. Open bag; punch down dough in bag. Reseal. Chill overnight, punching down occasionally. Divide into thirds. Do ahead: Wrap pieces separately; freeze up to 1 week. Thaw 2 pieces in refrigerator before continuing. Let 2 wrapped pieces stand at room temperature 1 hour before shaping.
5. For topping: heat 3 tablespoons oil in large skillet over medium-high heat. Add mushrooms; sprinkle with salt. Sauté until tender, about 5 minutes. do ahead Can be made 1 day ahead. Cool, cover, and chill.
6. Sprinkle 2 large sheets of parchment with flour. Roll out 2 dough pieces, each on separate parchment sheet, to 10-inch rounds, letting dough rest a few minutes if springing back.
7. Brush with oil; sprinkle each with 1/2 cup mozzarella and 1/3 cup Parmesan.
8. Top with mushrooms, then dot with goat cheese. DO AHEAD Slide pizzas on parchment onto baking sheets; cover with plastic. Chill up to 4 hours. Let stand at room temperature 30 minutes.
9. Position 1 rack in bottom third and1 rack in top third of oven; place heavy baking sheet on each and preheat oven to 450°F for at least 30 minutes.
10. Slide 1 pizza on parchment onto each hot baking sheet. Bake 8 minutes; reverse sheets. Bake pizzas until crusts are brown at edges and on bottom, about 10 minutes. Sprinkle with chives.

Makes two 10 inch pizzas.