Combine the warm water, yeast, and sugar in the bowl of a stand mixer fitted with the dough hook. Give it a quick stir to make sure that all of the yeast is able to dissolve in water. Allow it to sit for 5-10 minutes, until the yeast is foamy. Add the flour, 1/4 cup olive oil, and 2 tsp. sea salt and mix it on low until it has come together into a rough, shaggy dough. Turn the mixer up to medium and mix for 4-5  minutes, or until it’s a smooth. If the dough isn’t forming a ball and pulling away from the sides of the bowl, you can add flour 1/4 cup at a time until it’s sturdier. Once the dough has been kneaded, place it on a lightly floured surface and gently press it out. Sprinkle half of the chopped sundried tomatoes on the dough and fold the edges up around it. Repeat the flattening/folding with the rest of the tomatoes, then place the dough in a clean bowl. Cover it with a clean kitchen towel or cloth and set it somewhere warm (beside a sunny window works well!) to rise. Allow the dough to rise for about an hour, or until it has doubled in size. While it is rising, slice the onion and caramelize in the 1 Tbsp. of olive oil until soft and browned. Once the dough has risen, preheat the oven to 400F and line a large baking sheet with parchment paper. Turn the dough out onto the floured surface and roll out to a rectangle or round that is about 3/4″ thick. Move it to the parchment lined baking sheet and cover it again with the cloth. Allow it to rise for another 20 minutes, then poke it all over with your fingers to create dimples in the dough. Brush with the oil from the sundried tomatoes, then place the artichoke hearts and onions across the top of the dough. Drizzle with a bit more olive oil, then sprinkle with the large flake sea salt. Bake for 30 minutes, or until the edges are beginning to turn golden brown. Remove from the oven and serve warm.