The dough can be made in a food processor. Add nuts to bowl of food processor and chop into small pieces. Add the flour, sugar and salt to the bowl and pulse 3 or 4 times. Add the cold butter and again pulse, 8-10 times, until the dough has pea sized chunks of butter. Through the feeding tube add the egg and vanilla, pulsing 2-3 times. Finally add 3 tablespoons of ice water and pulse 6-8 times. If the dough looks dry, add 1 tablespoon of ice water at a time and pulsing 3 times. You should be able to see some butter chunks in the dough but it will be damp and somewhat sticky. Chill for at least 30 minutes.
After the dough has rested and is cold, roll out on a floured surface. Make sure you have a little flour on the rolling pin also. Once the dough is rolled out to approximately 12-inches, move to a parchment lined sheet pan. Note You always roll the dough out on the parchment and then move to a sheet pan.
Once the dough is rolled, assemble the berry filling. Combine all the berries in a bowl and toss with the lemon juice and zest, the 4 tablespoons of sugar, and the cornstarch. You will see berry juice in the bottom of the bowl. Have the crust ready for filling so that the berries do not leach too much liquid. With a slotted spoon, pile the fruit in the middle of the crust, making sure that there is a 1 ½ inch border of crust. Leave some of the berry juice in the bowl behind. The dough will leak if there is too much juice. Fold the border up and around the berries. If the dough has ripped while folding it, pinch it together to create a seal. Mix an egg with about 1 tablespoon of water and brush on the dough . Sprinkle sugar over the top of the galette.
Baking the Galette
This is a very rustic looking dessert. It is okay if it isn't perfect. Bake in the oven for approximately 40 minutes, until the crust looks golden brown. Check after 30 minutes to see the progress of the dough. Adjust the cooking time if the galette looks like it is getting close to be done. Let cool until room temperature.
Add the brown sugar to the creme fraiche. Adjust the sweetness to your liking. Top each galette slice with a dollop.
Making the dough by hand - Chop the nuts into small pieces and place in a bowl. Add the flour, sugar, and salt to the nuts, mixing until fully incorporated. Add the cold butter cubes into the dry ingredients. Using your hands or a pastry fork, smash the butter into the flour mix. Stop when the butter is the size of peas. Add the vanilla, the egg, and 3 tablespoons of ice water at once. Mix until the dry ingredients start to come together and will form a ball when squeezed in your hand. If you need more water, add 1 tablespoon at a time. The dough is somewhat wet and sticky and you should see some butter pieces. Chill for 30 minutes.