To make crust: In a large bowl, whisk together the flour, yeast and salt. Make a well in the center and pour in the oil, 1 egg and ¼ cup water. With a fork, begin beating the wet ingredients, slowly pulling in the dry ingredients until a soft dough forms. Knead in the bowl until the ball of dough holds together, then transfer it to a lightly floured surface and knead for a couple of minutes. The dough should be soft but not sticky. If it's sticky, add a little flour and knead again. Wrap in plastic wrap and set aside while preparing filling.
Preheat oven to 350 degrees.
To make filling: Peel squash, making sure to peel down to the deep orange flesh, then seed and slice into ½-inch thick discs. Place on lightly oiled baking sheet, brush with 1 tablespoon olive oil and sprinkle with thyme. Roast for 20 to 30 minutes, or until tender. Set aside to cool slightly. Leave oven on.
Stem and wash chard, then tear into 3-inch pieces. Heat remaining olive oil (use any leftover from squash) and sauté chard, stirring frequently until just wilted, about 4 minutes. Set aside.
Grate cheeses and set aside.