In a small bowl, combine the yeast, sugar, and warm water. Allow to sit for 5 minutes, until the yeast “blooms” and small bubbles form.
Pour mixture into a standing mixer fitted with the hook attachment. Stir in oil and salt, then incorporate flour with your hands. Mix on low speed for about 10 minutes. You want your dough to look shiny and smooth. If it looks dry, add in an additional tablespoon of water.
Grease a large bowl with more oil and place the dough into the bowl. Cover the bowl with a kitchen towel and place in a warm area to rise until doubled in size, about 1 hour.
Preheat oven to the highest heat setting (mine was 550°F). Line a cookie sheet with parchment paper. Place the risen dough in the middle of the cookie sheet. Pat the dough with the palm of your hand to flatten it slightly. Now, using your fingertips, spread the dough into a 13 inch circle. Start by pushing in the middle of the dough and working your way out, making sure to leave a 3/4 inch lip of dough around the edge for your crust. Brush dough with 1-2 tablespoons of olive oil.
In a blender, combine the crushed tomatoes and salt, pulsing until emulsified. Spread the sauce onto the dough. Top with zucchini, then with portions of mozzarella. Place the squash blossoms in a circular pattern around the pizza.
Bake the pizza for 10-12 minutes (depending on your oven) until the crust is golden brown and the cheese is melted. Cut into pieces and serve!