Add all of the dough ingredients into a stand mixer. Beat with a dough hook for 4-5 minutes, until it forms a dough ball.
Place the dough ball on the counter, and place the bowl upside down over the dough to let it rise. It should double in size in about 1 1/2 to 2 hours. While it's rising, prepare the other ingredients.
Cut the dough in half. Refrigerate in an oiled plastic bag up to one week or grill right away.
Guinness Caramelized Onions
Heat the grill to medium. Place a cast-iron skillet over direct heat. Heat the olive oil and butter.
Add the sliced onions and sauté 15-20 minutes until wilted, stirring occasionally.
Add the Guinness, salt and sugar and continue cooking for another 5-10 minutes, stirring often until golden brown. Set aside.
Guinness Sausage
In a medium bowl, whisk together the egg and Guinness. Tear the bread into dime-size pieces, and add to the bowl with all of the herbs and spices and garlic. Mix well.
Mix in the ground pork – go on; get in there and use your hands.
Refrigerate at least 30 minutes.
Shape the meat into seven sausage links – no need to case them.
Heat the grill to medium-high heat (~350 degrees). Oil the grates. Grill the sausages for 20 minutes, turning occasionally.
Let rest 10 minutes; slice.
Guinness Glaze
Place the ingredients in a medium sauce pot. Bring to a boil. Reduce to a simmer. Simmer over low heat for about 30 minutes, stirring occasionally. It will register about 140F on a candy thermometer and will coat the back of a spoon.
Make The Pizza
Heat the grill to about 450 degrees with a pizza stone set over indirect heat.
Sprinkle cornmeal onto a pizza paddle. Stretch half of the dough out to your desired size and place on the paddle, making sure there is enough cornmeal so that it will easily slide onto the grill.
Drizzle olive oil on the dough. Sprinkle with half of the shredded Fontina cheese.
Top with half of the Guinness caramelized onions and sliced grilled Guinness sausage. Add half of the fresh mozzarella on top.
Slide onto the pre-heated pizza stone. Grill for about 10 minutes. The crust should be golden and the cheese melted. Remove with the pizza paddle.
Drizzle with Guinness glaze and sprinkle with Walter Imperial Stout salt and fresh green onions. Slice and serve. Repeat with the remaining ingredients to make a second pizza.