Place wholegrain spelt flour and salt in a large mixing bowl and whisk to combine. Cut in the cold butter and mix with your fingertips until the mixture resembles coarse crumbs. Drizzle ice water into the bowl and continue to mix ingredients with your fingertips. Turn out the dough onto your work surface and gather the dough into a ball. Wrap the ball with a plastic film and flatten the dough into a thick round. Chill in the fridge for at least one hour, or up to two days.
Preheat oven to 200C/400F. Roll out the dough between two pieces of parchment paper to form a 15-inch circle. Sprinkle half of Parmesan and Gorgonzola in the center, leaving 2-3 inches border all around. Then mound the red wine spinach, roasted mushrooms, and beet on the top of cheeses.
Fold the border up and over the filling to form a rim, pleating as necessary. Now sprinkle the remaining Parmesan and Gorgonzola over the vegetables. Brush egg glaze over the rim.
Bake the galette until the crust is nicely golden brown, about 30-35 minutes. Let cool on the baking sheet on a wire rack for 5 minutes. Slide onto a serving platter and sprinkle some garden cress over. Serve hot or at room temperature.