Begin by making the crust. Mix together all of the dry ingredients in a large bowl. Then cut the butter into pea-sized pieces over the dry ingredients. Add the water and honey to the bowl and knead the dough together with your hands until all of the ingredients are well-blended together and there are no chunks of butter left in the dough. Shape the dough into a ball, cover, and refrigerate it.

Preheat the oven to 375 degrees Fahrenheit. Take the dough out of the refrigerator and place it on a well-floured surface. Roll it out into a circular shape until it is about 1/3 inch thick. Transfer it onto a well-greased baking pan and set it aside.

Mix together all of the dry ingredients in a large flat bowl until completely blended. Drain the pear slices and pat them dry with a paper towel. Add the pear slices, berries, and vanilla extract to the bowl and toss them in the dry ingredients until they are evenly coated in the sugary mixture. Pour the filling onto the middle of the crust, leaving at least 3 inches of crust-space around the filling.

Fold the edges up over the filling and tear off any extra crust so that the crust border is no more than 4 inches wide, (this way you can expose more of the pretty filling). Cut up the teaspoon of butter into pea-sized pieces and evenly distribute them over the exposed surface of the filling. Place the galette in the oven and bake for 30 minutes, then remove it and lightly brush some of the whisked egg over the exposed surfaces of the crust. Place the galette back in the oven and bake for another 30 minutes, or until the crust is a nice and shiny golden brown. Remove the galette from the oven and allow it to cool for 45 minutes before serving.