Preheat oven to 480 degrees F.
Heat a large saute pan over medium heat. Add olive oil and heat. Add garlic, shallot and mushrooms and cook for 4 minutes. Add spinach and cook until spinach is very tender, roughly 6 minutes. Fold in the goat cheese, season with salt, to taste, and let cool. Lay out phyllo dough, butter liberally and fold into fourths. Butter again.
Divide mushroom and spinach mix into 4 equal parts on the phyllo. Fold into triangles buttering between each fold. Bake for 8 minutes or until golden brown.