Add the sugar to 1/2 cup (125 mL) warm water, stirring to dissolve.
Add the yeast, stir to blend and let sit for 5 minutes or until frothy, then add oil.
Measure flour, salt and ground flax seed in a large bowl, stir to blend, then add sugar, water and yeast mixture; stir to make soft, slightly sticky dough.
Knead until elastic and very smooth.
Transfer to an oiled bowl, turning to coat dough on all sides. Cover with plastic wrap and let stand in warm draft-free place until doubled in size, approx. 1 hour.
Punch the dough down and wrap in plastic or use immediately.
Pre-heat oven to 450°F (260°C). Roll or pat the dough out to a 12 inch (30 cm) circle on a clean, floured surface and transfer to a baking sheet.
Heat a skillet over medium high heat. Add 1 tbsp olive oil, garlic and mushrooms and sauté until soft, approx. 7 minutes. Season with salt and pepper.
Brush dough with remaining olive oil, sprinkle with shredded cheese, mushroom mixture and goat cheese.
Bake for 20 minutes until crust is crispy and golden. Top with fresh arugula and drizzle with olive oil to serve.