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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.
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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
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3
Heat 3 tablespoons oil in large skillet over medium-high heat. Add mushrooms; sprinkle with salt. Saute until tender, about 5 minutes. do ahead Can be made 1 day ahead. Cool, cover, and chill.
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4
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
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5
Position 1 rack in bottom third and1 rack in top third of oven; place heavy baking sheet on each and preheat oven to 450u00b0F 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.