Start by making the crust. Remove flour from freezer and transfer to a large bowl; add salt and whisk together. Place butter pieces in flour (try to do it in an even layer so they don't stick together too much) and use a pastry blender to combine until mixture forms a coarse meal.
In a small bowl, whisk together sour cream, lemon juice, and ice water. Add wet mixture to flour mixture and mix together using a wooden spoon until large lumps form. Pat into a ball (don't overwork it!) and cover bowl with plastic wrap. Refrigerate for 1 hour.
While crust is chilling, start the filling. (Ooh, it rhymes!) Heat olive oil in a large skillet over medium heat. Add onions and sauté, stirring frequently, for 3 minutes, or until softened. Stir in brussel sprouts and continue to stir frequently. Cook until just beginning to brown, 7–8 minutes. Remove from heat and stir in 1 tablespoon of vinegar, walnuts, grapes, salt, and pepper. Cool vegetable mixture before adding it to the crust—this is important!
Now let's get back to the crust. Preheat oven to 400°F. Roll out galette dough on a floured surface until it forms a 12-inch round. Carefully transfer to baking sheet. Leaving a 2-inch border on all sides, sprinkle crust with Parmesan cheese and add brussel sprout mixture on top of cheese. Fold edges of crust over the filling and brush crust with egg yolk mixture. Bake for 30 minutes or until crust is golden brown.
While galette is baking, make the balsamic reduction. Heat remaining balsamic vinegar in a small saucepan over medium-high heat, whisking constantly, for 8–10 minutes or until it forms a syrup. Drizzle syrup over galette when it's finished baking.
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