In a mixing bowl, combine the lukewarm water, sugar, and active dry yeast. Let this mixture sit for about 5-10 minutes until it becomes frothy.
In another bowl, whisk together the whole wheat flour and salt.
Once the yeast mixture is frothy, pour it into the bowl of dry ingredients. Stir until a shaggy dough forms.
Transfer the dough onto a floured surface and knead it for about 5-7 minutes until it becomes smooth and elastic.
Place the kneaded dough into a lightly greased bowl, cover it with a clean kitchen towel, and let it rise in a warm area for about 1 hour or until it doubles in size.
Preheat your oven to 475°F (245°C) while the dough is rising.
Once the dough has risen, punch it down to release any air bubbles. Roll it out on a floured surface to your desired thickness.
Transfer the rolled-out dough onto a baking sheet or pizza stone. Spread the pesto sauce evenly over the surface, then sprinkle the mozzarella cheese, followed by spinach, mushrooms, and cherry tomatoes.
Bake the pizza in the preheated oven for about 12-15 minutes or until the crust is golden brown and the cheese is bubbly.
Remove the pizza from the oven, let it cool for a few minutes, slice it up, and enjoy your delicious homemade whole wheat pizza!