Combine buckwheat, water, oregano, and 1 teaspoon olive oil in a bowl; mix until well combined.
Heat 1 teaspoon olive oil in a skillet over medium-high heat. Add half of the tortilla batter; cook until edges are dry, about 2 minutes. Flip and cook until browned on the other side, 2 to 3 minutes more. Transfer to a baking sheet. Repeat with remaining batter.
Place diced tomatoes and garlic in the same skillet over medium heat; bring to a boil. Reduce heat and simmer until soft, about 5 minutes. Spread tomato mixture over tortillas and top with tomato slices, spinach, and nutritional yeast.
Bake in the preheated oven until golden, about 10 minutes.