First, proof the yeast in ½ cup of warm water for about five minutes until fluffy and fragrant.
Add the yeast mixture, the rest of the water, the bread flour, and the salt to the bowl of a stand mixer and use the dough hook to knead for ten minutes, until smooth. Let rest for 10 minutes, then knead for 5 more.
Add ¼ cup of olive oil to a large bowl, and transfer the dough to the bowl. Let rise for 2 hours in a warm place.
Add ¼ cup more olive oil to a large, lipped half sheet tray. Transfer the dough to the sheet tray and stretch to the edges of the tray as best you can. Drizzle the remaining ¼ cup of olive oil on top of the dough, and then cover and let rest for 15 minutes before stretching again.
Set aside in a warm place for 1 hour and let rise. Meanwhile, preheat the oven to 450F.
Use your fingers to make dents in the top of the dough, then spoon the pesto over top of the focaccia, using a spoon to distribute it evenly.
Bake the focaccia for 25 minutes, until golden brown.
