In a mixing bowl, combine the lukewarm water, active dry yeast, and sugar. Stir gently and let it sit for about 5-10 minutes until bubbly and frothy.
In another bowl, mix the whole wheat flour and salt.
Once the yeast mixture is frothy, gradually add the dry ingredients to the bowl. Stir until a shaggy dough forms.
Transfer the dough onto a lightly floured surface and knead for about 5-7 minutes, until smooth and elastic.
Place the kneaded dough in a lightly greased bowl. Cover it and let it rise in a warm place for about 30 minutes or until it doubles in size.
While the dough is rising, preheat your oven to 475°F (245°C).
Once the dough has risen, punch it down gently and roll it out to your desired thickness.
Spread the pesto sauce evenly over the crust, then sprinkle the mozzarella cheese, spinach, mushrooms, and cherry tomatoes on top.
Transfer the topped pizza to the preheated baking sheet or pizza stone. Bake for 12-15 minutes or until the crust is golden brown.
Once baked, remove the pizza from the oven and let it cool for a couple of minutes. Slice and serve!
