Add the cherries to a storage container. Add the remaining cherry ingredients to a saucepan over medium high heat, stir to combine. Bring to a boil, remove from heat. Pour the pickling liquid over the cherries. Cover and refrigerate for at least 2 hours and up to 3 days.

In the bowl of a stand mixer fitted with a dough hook attachment, add the flour, yeast, garlic powder and sugar.

Mix until combined. Heat the beer until the temperature reaches between 120°F and 125°F (double check your yeast package to confirm this is the temperature your yeast needs. Default to the temperature listed on the package).

Add the beer to the stand mixer and mix on medium speed. Once most of the flour has been moistened, slowly add the salt and oil while the mixer is still running. Turn speed to high and beat until dough is smooth and elastic, about 8 minutes. Transfer dough to a lightly oiled bowl, tightly wrap with plastic wrap. Allow to sit in a warm room until doubled in size, about 45 to 60 minutes.

Add a pizza stone to the grill, heat the grill to 500°F.

Roll the dough out on a lightly floured surface to about 10-inches in diameter, add to a pizza peel covered with semolina flour or corn meal. Cover with pizza sauce, cheese, squash blossoms and cherries. Carefully transfer to the pizza stone. Shut the lid and allow to cook until the top of the crust is bubbly and starting to brown, about 6-8 minutes.

Remove from the grill, transfer to a serving platter, top with pea shoots and basil. Slice and serve.