Pour 1/4 cup warm water into large bowl. Sprinkle yeast over; stir to blend. Let stand until yeast dissolves and mixture is slightly foamy, about 10 minutes. Stir 1 1/2 cups room-temperature water and salt into yeast mixture. Add 3 1/2 cups flour, 1/2 cup at a time, stirring until slightly sticky dough forms. Knead dough on floured surface until smooth and elastic, adding more flour by tablespoonfuls if sticky, about 10 minutes. Oil large bowl. Add dough; turn to coat. Cover bowl with plastic wrap. Let rise in warm area until doubled in volume, about 50 minutes. Punch dough down; turn out onto floured surface. Divide dough into 4 equal pieces; knead each briefly until smooth. Cover with towel; let rise until almost doubled, about 30 minutes. Prepare barbecue (medium-high heat). Roll out 1 dough piece on lightly floured surface to 11 x 8-inch rectangle. Transfer to floured baking sheet. Brush top with oil. Place oiled side down on barbecue. Grill until bottom is golden, about 2 1/2 minutes. Brush top with oil. Using tongs, turn bread over; grill until second side is golden, about 2 minutes. Transfer to baking sheet. Brush bread with oil. Repeat with remaining dough pieces. (Can be made 4 hours ahead. Cover with foil; let stand at room temperature. Before continuing, prepare barbecue; use medium-high heat.) Sprinkle Parmesan and Fontina over breads. Top each with tomato slices, corn kernels, parsley and jalapeno. Drizzle with oil. Place breads on barbecue; cover loosely with foil. Grill until cheese melts, watching closely, about 2 minutes. Cut each bread into pieces; serve warm.