For the dough: Mix the sugar and yeast in 1 1/2 cups warm water (100 to 110 degrees F).
Let sit until foamy, 3 to 5 minutes.
Stir in the olive oil. In a mixer fitted with the paddle attachment, combine the yeast mixture with the flour and salt and mix on low until smooth.
Switch to the dough hook and knead on medium, adding a little more flour or water if needed, until the dough forms a loose, sticky ball around the hook. Increase the speed to medium-high and knead until the dough is soft, smooth and springy, 2 to 3 minutes.
Put the dough in a large bowl, drizzle with olive oil and turn to coat. Cover with plastic wrap and let rise until doubled in size, about 1 1/2 hours.
For the topping: Meanwhile, in a food processor, combine the basil, pine nuts, garlic and 3 cups of the arugula. Process to make a chunky paste. Add 1/4 cup olive oil and process until smooth. Add the Parmesan and pulse just until incorporated. Season lightly with salt and pepper.
In a medium skillet, cook the bacon until crisp. Drain on paper towels.
When the dough has risen, preheat the oven to 500 degrees F with a baking stone on the bottom rack.
Punch down the dough. Brush an 18-by-13-inch rimmed half-sheet pan liberally with olive oil. Transfer the dough to the pan and press it all the way into the corners (it helps to cover the dough with a sheet of plastic wrap while pressing so the dough doesn't stick to your fingers).
Bake on the preheated stone until the dough has puffed and just begins to color, 8 to 10 minutes.
Remove the dough from the oven, loosen from the baking sheet with a metal spatula and brush lightly with olive oil. (The crust can be baked ahead to this point and topped and finished in the oven later, if desired.)
Spread the pesto on the dough almost to the edges. Top with the mozzarella, feta, artichokes, cooked bacon and jalapeno slices.
Bake on the top rack until the cheese is browned and crusty, about 8 minutes more.
In a large bowl, toss the remaining 3 cups arugula with the remaining tablespoon olive oil and the jalapeno brine. Season with salt and pepper and scatter over the pizza. Cut into squares to serve.
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Tools You May Need
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