Mix yeast, sugar, and warm milk in a cup. Set aside for 5 minutes to activate. Add 1 teaspoon of rice flour, 1 teaspoon oat flour and 1 teaspoon gluten-free all-purpose flour. Mix and set aside for 20 minutes.
Sift the rest of the flours into a large bowl, add the melted butter and salt. Gradually add milk with dissolved yeast, mixing well to form a soft dough. Transfer the dough to a lightly floured work surface. Knead for five minutes until smooth and elastic. Transfer the dough back to the large bowl, cover with a cotton cloth and let rise for about 30-45 minutes, until it has doubled in volume.
Preheat the oven to 425°F.
When the dough has risen, roll it out into a circle 10 inches in diameter with slightly higher edges. Transfer the dough to a baking sheet lined with parchment paper. Place the pizza in the oven for 3-5 minutes.
Remove from the oven and spread the passata on the surface of the pizza. Sprinkle with crushed garlic and sliced mushrooms. Arrange the mozzarella over it and sprinkle with Gouda cheese. Add the tomatoes and bake for 15-20 minutes, until the edges are lightly browned.
Remove from the oven. Drizzle with olive oil and sprinkle generously with arugula. Serve hot.