Step 1: Preheat oven to 350°F. Line a baking sheet with parchment paper.
Step 2: Heat a medium-size skillet over low-medium-low heat and add 1 tablespoon olive oil. Add 1 medium-size onion and 1 to 2 pinches salt and cook, stirring every 5 minutes, until caramelized, about 30 minutes total. Add water, as needed, if onion begins to dry out. Remove from heat and cool slightly.
Step 1: While onions are caramelizing prepare galette dough, cut 8 tablespoons butter into pea-size pieces and 2 cups flour with a pastry cutter or food processor until you have a coarse meal. Add pinch of salt. Stir with fork/process continuously while slowly adding 6 tablespoons ice water, 1 tablespoon at a time, until dough sticks to itself. Form into a ball of dough, then roll out onto a flour-dusted surface into a 10-inch round. Transfer rolled-out dough to prepared baking sheet.
Step 1: First scatter cooled, caramelized onion in center of dough circle, leaving about a 1-inch rim of uncovered dough all around. Scatter 1 1/2 cups mixed green and red grape in a single layer over onion. Mix together 1 cup crumbled feta and 1 teaspoon fresh minced rosemary with your fingers or a spoon, then scatter among grapes.
Step 2: Now, fold over uncovered rim of dough to encase filling, slightly overlapping each segment. Lightly brush rim of crust with a small amount of cold water. Sprinkle remaining salt and 2 pinches pepper onto water-glazed crust and over galette filling. Drizzle a small amount of olive oil over filling.
Step 3: Bake for 40 to 45 minutes until grapes are roasted, crust is golden, and cheese starts to brown.