Puree sour cream, milk, and butter in a food processor. Add dry ingredients and gruyere and pulse briefly several times to combine. Do not overmix! Mixture will be moist and somewhat clumpy.
Remove dough and place on a flat surface dusted with flour.
Knead several times and press dough out into a round 8” circle. Sprinkle flour on top of surface and pat so that dough is not sticky. Cover with plastic wrap and refrigerate for at least 20 minutes while preparing filling.
Filling
Preheat oven to 400°F (204°C).
Heat oil over medium-high heat. Add leeks and cook for 2-3 minutes until leaks are starting to become soft. Add garlic and cook a minute longer.
Add mushrooms and cook for 4-5 minutes until mushrooms have cooked down and most of the water content has evaporated. Add kale and cook down for a minute or two until wilted. Remove from heat.
In a separate bowl, whisk the egg, sour cream, salt, and pepper together. Add this mixture to the cooked leeks and mushrooms along with the parsley, and rosemary.
Assembly
Remove the dough from the refrigerator and place on floured flat surface. Use a floured rolling pin to roll into a ¼ inch thick circle approximately 14 inches in diameter. Add filling to center of dough circle leaving a 2 inch border along the edge.
Fold the border up around the edges. Spray a baking sheet with oil and move galette onto prepared sheet. Bake for 25 – 30 minutes until crust is starting to brown. Remove from oven and let cool for 10 mins before serving.