Prepare squash: Preheat oven to 375 degrees F. Peel squash, then halve and scoop out seeds. Cut into a 1/2-inch dice. Toss pieces with olive oil and a half-teaspoon of the salt and roast on foil lined (for neatness sake) sheet for 30 minutes or until pieces are tender, turning it midway if your oven bakes unevenly. Set aside to cool slightly. Or you can use roasted mashed squash.
Caramelize onions: While squash is roasting, melt butter in a heavy skillet and cook onion over low heat with the remaining half-teaspoon of salt and pinch of sugar, stirring occasionally, until soft and lightly golden brown, about 45 minutes. Stir in cayenne.
Raise the oven temperature to 400 degrees. Mix squash, caramelized onions, cheese and herbs together in a bowl.
Assemble galette: On a floured work surface, roll the dough out into a 12-inch round. Transfer to a pie plate. Spread squash, onions, cheese and herb mixture over the dough, leaving a 1 1/2-inch border. Fold the border over the squash, onion and cheese mixture, pleating the edge to make it fit. The center will be open.
Bake until golden brown, 30 to 40 minutes at 400 degrees. Remove from the oven, let stand for 5 minutes, then slide the galette onto a serving plate. Cut into wedges and serve hot, warm or at room temperature. Serves 6.