Pulse flour and salt in a food processor. Add butter pieces and pulse to form a mixture resembling small peas. Add ice water one tablespoon at a time. pulsing until dough mostly sticks together.
Transfer to a lightly floured surface. Shape dough into a disk. wrap tightly in saran wrap, and refrigerate for at least 30 minutes.
Heat oven to 400 •F. Toss butternut squash with two tablespoons olive oil. Stir in thyme, salt & pepper. Spread on baking sheet, add head of garlic to sheet, cut side down, and bake in oven. After 25 minutes, pour wine over veggies on baking sheet. return to oven. Continue to cook until squash and garlic are tender and beginning to brown, about 30 minutes.
Squeeze individual roasted garlic cloves out head, and combine with goat cheese in a bowl.
Heat two tablespoons of olive oil in pan over medium heat. Add onions and a pinch of salt. Cook onions, stirring occasionally until they soften and caramelize into a deep brown. Turn down heat if onions brown too quickly or begin to burn. Add honey, mix to combine. Turn off heat. set onions aside to cool.
Line baking sheet with parchment paper. Roll out on a lightly floured surface to about¼ inch thick. Transfer to baking sheet.
Spread garlic cheese mixture over dough, leaving a 1-inch border. Top with caramelized onions. then butternut squash, maintaining border. Fold edges of dough towards the center and pinch to hold in place. Top with parmesan cheese.
Bake galette at 400·F until crust is crisp and golden brown, about 25 to 30 minutes. Garnish with fresh thyme leaves and serve warm.