Ingredients

• 2 1/2 cups unbleached all purpose flour or bread flour
• 1/2 cup white whole wheat flour or bread flour
• 3 tablespoons vital wheat gluten flour or bread flour
• 1 1/2 teaspoons coarse kosher salt
• 1 teaspoon sugar
• 1 cup plus 2 tablespoons warm water (105°F to 115°F)
• 1 1/2 teaspoons active dry yeast
• 3 1/2 tablespoons extra-virgin olive oil, divided
• Additional unbleached all purpose flour (for kneading and shaping)
• 3 tablespoons extra-virgin olive oil plus additional for brushing
• 6 ounces fresh shiitake mushrooms, stemmed, thinly sliced
• 6 ounces fresh chanterelle mushrooms, thinly sliced
• 1 cup (packed) coarsely grated whole-milk mozzarella cheese
• 2/3 cup freshly grated Parmesan cheese
• 6 ounces chilled soft fresh goat cheese, coarsely crumbled
• 2 tablespoons sliced fresh chives

Instructions

1. 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. 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.
2. 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. 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.
3. 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.
4. 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.
5. 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. Brush with oil; sprinkle each with 1/2 cup mozzarella and 1/3 cup Parmesan. 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. 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. 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.
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. Brush with oil; sprinkle each with 1/2 cup mozzarella and 1/3 cup Parmesan. 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.
7. 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. 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.