Warm the milk to 100-105 degrees F, and place in a small bowl. Stir 2 teaspoons sugar into the milk and sprinkle the yeast over. Set aside for 5-10 minutes, until mixture is bubbly.
Place the flour, 1 tablespoon olive oil, and 1 teaspoon salt in the bowl of a standing mixer and mix together briefly using the dough hook. Add the yeast/milk mixture and begin to knead, adding the water gradually. The mixture should come together as a soft, stretchy dough, pulling away from the sides of the bowl. Add a bit more flour if mixture is too wet, and add a bit more water if mixture seems dry, crumbly, or overly stiff. Knead for 5-10 minutes, until dough is smooth, soft and elastic.
Oil a bowl with olive oil and place the dough in the bowl. Cover with plastic wrap and let dough rise until doubled in size.
While the dough is rising, peel and slice the onion into very thin strips. Heat 1 tablespoon olive oil in a heavy skillet over low heat, and add the onions. Season onions with 1/4 teaspoon salt and a teaspoon of sugar. Cook onions over low heat, stirring occasionally, until onions turn caramel brown and fragrant, about 15 minutes.
Remove onions from skillet and set aside. Place another tablespoon of olive oil in the same skillet. Cook the garlic, chopped red pepper, and chopped green onions over medium heat in the skillet until soft and fragrant. Add the coarsely chopped spinach, along with 1 teaspoon garlic salt, and sauté spinach with the other vegetables, stirring, until the spinach is completely wilted. Remove skillet from heat, and transfer vegetable mixture to a colander, allowing excess liquid to drain away.
Once the dough has risen, punch it down and divide dough into two pieces. Roll each half into a smooth ball. Pour 2 tablespoons of olive oil into a 12-inch pizza pan or cast iron skillet. Place one ball of dough in the middle of the pan and flatten gently with your fingers. Let dough relax for 10 minutes.
Continue to flatten dough into the pan, pressing and pushing it toward the sides of the pan, letting it relax in between, until dough covers the bottom of the pan. Oil the counter and roll the other piece of dough into a 12-inch circle, letting it relax on the counter until it holds its shape.
Preheat oven to 450 degrees. Whisk the cream cheese and Boursin together, heating them for a few seconds in the microwave if needed. Spread the cheese mixture over the dough in the pan/skillet, leaving a half inch border around the edge. Cover the cheese spread with the spinach/vegetable mixture in an even layer. Spread half of the mozzarella cheese over the vegetables, and sprinkle with 2 tablespoons of grated Parmesan. Place the other round of dough over the cheese and seal the edges of the two dough circles together.
Top the pizza with the caramelized onions. Cover the onions with the remaining mozzarella, and sprinkle with the dried oregano and the remaining 2 tablespoons of Parmesan cheese.
Place the fugazzeta in the oven. Bake for 20-25 minutes, or until the edges are golden brown and crispy.
Remove from the oven. Let cool for 5-10 minutes before cutting into slices to serve.
