Dough
Warm the mixing bowl of a stand mixer with the paddle attachment. Add the yeast and sugar and dissolve them in the warm water. Add the 2 cups flour and mix at medium speed for 2 minutes. Cover the bowl with plastic wrap and let rest at warm room temperature for 10 minutes. Then add the sour cream, butter, and salt and mix the dough at medium speed for about 10 minutes; it will look shaggy at first, but eventually it will come together in the mixing bowl. If the dough still seems sticky, beat in 1 to 2 tablespoons additional flour. Leave the dough to rise for 1 hour in the mixing bowl, covered with plastic wrap, or transfer to a plastic bag to rise. The dough is now ready to use. You can also refrigerate it to use within 2 days, letting it come to room temperature before making pizza; or freeze it for later use, thawing it overnight in the refrigerator and then letting it come to room temperature.

Sauce and Toppings
Heat the olive oil in a saucepan over medium heat; add the garlic and sauté 1 to 2 minutes. Stir in the tomato paste and then the water, stirring until smooth. Stir in the oregano and brown sugar until the sugar dissolves. Set aside.

Preheat the oven, ideally with a pizza stone or baking tiles on the center shelf, to 500°F.

Divide the dough into 2 equal pieces. On a lightly floured work surface, partially roll one dough piece, and then, with clean hands, stretch and shape it into a round or rectangular pizza shape. Spoon half the sauce onto the dough, spreading it evenly while leaving a narrow uncovered rim; then spread half the mozzarella cheese and top with half the pepperoni.

Transfer the pizza to parchment paper and place on the hot pizza stone. Bake until the cheese is melted and bubbling and the crust is deep golden brown, 8 to 9 minutes. While the pizza is baking, toss the arugula with the lemon juice and olive oil.

Remove pizza from the oven and leave it to cool for 2 minutes. Garnish with half of the arugula in the center, cut, and serve. Prepare the second pizza the same way.