Proof the yeast: In a mixing bowl, combine 3/4 cup warm water, 1 teaspoon sugar, and 1 teaspoon active dry yeast. Let it sit for 5–8 minutes until foamy. If nothing happens, your yeast may be dead—start over with fresh yeast.
Make the dough: Add 1 3/4 cups flour (start with 1 1/2 cups if using all-purpose), 1 teaspoon kosher salt, and 2 tablespoons olive oil to the yeast mixture.
Stir until shaggy. The dough should be soft and slightly sticky, not dry.
Knead briefly: Knead on a lightly oiled surface for 2–3 minutes, just until smooth. If it’s too sticky to handle, add a tablespoon of flour at a time, but keep it on the tacky side for better texture.
First rise: Place the dough in a lightly oiled bowl, cover, and let it rise in a warm spot for 45–60 minutes, or until doubled.
A warm oven (off) with the light on works well.
Prepare the pan: Line the air fryer basket with parchment or use a 7–8 inch round cake pan that fits your air fryer. Generously oil the parchment or pan with 1–2 tablespoons olive oil.
Shape the dough: Transfer the risen dough to the prepared pan. Gently press and stretch it to the edges.
If it springs back, let it rest for 5 minutes and try again.
Dimple and top: Drizzle 1–2 tablespoons olive oil over the dough. Use your fingertips to press deep dimples all over. Spread 2–3 tablespoons pesto in swirls.
Nestle halved cherry tomatoes cut-side up into the dimples. Sprinkle with 1 small grated garlic clove, a pinch of dried oregano, and a little kosher salt.
Second rise: Let the topped dough rest for 15–20 minutes. This helps it puff for a lighter crumb.
Air fry: Preheat the air fryer to 350°F.
Air fry for 12–16 minutes until the top is deep golden and the internal temp reaches about 200–205°F. Rotate the pan halfway if your air fryer browns unevenly.
Finish: Brush with a bit more olive oil. Sprinkle flaky sea salt, a pinch of red pepper flakes, and grated Parmesan if you like.
Let it cool for 5–10 minutes before slicing.