For the no-churn vanilla ice cream: Add the sweetened condensed milk and mascarpone to the bowl of a stand mixer fitted with the whisk attachment (or use a hand-held electric mixer) and whip until smooth and combined. Add the heavy cream, vanilla and salt. Whip until stiff peaks form. Spoon the ice cream into a freezer-safe container and freeze 6 hours or overnight.
For the crust: Combine the flour, cornmeal and salt in a large bowl. Add the butter and use your fingers to break the butter into the flour until the mixture has butter chunks the size of small peas. Add 3 tablespoons cold water and mix with a wooden spoon, drizzling in more water as needed (no more than 1 tablespoon at a time), until the dough just comes together (a few dry spots are okay). Gently knead the dough on a lightly floured surface until no dry spots remain, about 1 minute. Cover the dough and place it in the fridge while you prepare the filling, at least 15 minutes (the dough keeps, covered, refrigerated, for up to 1 week).
For the filling: Line a baking sheet with parchment paper and set aside. In a bowl, toss together the berries, brown sugar, flour, lemon juice and vanilla bean seeds.
Flour the work surface and roll the dough to about 1/8-inch thick. Transfer to the prepared baking sheet. Spoon the berries over the dough leaving a 3-inch border around the edges. Pour any remaining juices left in the bowl over the fruit. Fold the edges of the dough over the filling. Brush the crust with the beaten egg and sprinkle the coarse sugar over the dough.
Place the galette in the fridge for 30 minutes, or until ready to bake, no longer than 2 hours.
Preheat the oven to 400 degrees F. Bake the galette until the crust is golden and the fruit is soft and caramelized, 40 to 45 minutes. Allow to cool slightly. Serve warm or at room temperature with a large scoops of ice cream and a drizzle of honey.