In a bowl, combine warm water, yeast, and honey. Let sit for 5 minutes until bubbly.
Whisk flour and salt in a stand mixer bowl. Stir ¼ cup olive oil into yeast mixture, then add to flour. Mix until combined.
Knead with dough hook on medium speed 7 minutes, adding flour 1 tablespoon at a time if needed. Dough should be smooth and slightly sticky.
Place in oiled bowl, cover, and rise until doubled, about 1 hour.
Press dough into an oiled 9×13-inch baking sheet. Dimple surface and brush with 2 tablespoons olive oil. Rest 30 minutes.
Preheat the oven to 450°F.
Caramelize onions in olive oil over medium heat for about 20 minutes. Stir in balsamic and maple syrup; cook 2 minutes more.
Press strawberries into dough. Top with onions, basil, remaining olive oil, and sea salt.
Bake for 20 minutes until golden. Cool 5 minutes before slicing. Add goat cheese if desired.