Preheat oven to 500 degrees F (with pizza stone if you have one).
Stir water and yeast together in a bowl until well-combined.
Add flour, salt, honey and pureed beets to the yeast mixture and mix together.
Turn the dough out onto a floured countertop and knead it until the flour is mixed inches If the dough is too sticky, add more flour until it's workable.
Form dough into a ball and place in an oiled bowl. Cover with plastic wrap and let rise in a warm place for 2 hours.
When it's doubled in size, divide dough in half for two 12-inch crusts (or refrigerate one of them for later).
Grease a piece of parchment paper and stretch the dough out on top of it. Place another piece of parchment on top of the dough and use a rolling pin to flatten the dough further to 1/4-inch thickness.
Top the dough with a thin layer of pesto. Then add mozzarella (sliced or shredded), sliced beets, asparagus and sliced cherry tomatoes. Bake pizza on a pizza stone or baking sheet for 5-8 minutes or until crust is lightly brown.
Remove from oven and garnish with soft-boiled eggs and arugula.