Toss cherry tomatoes in oil, salt and pepper and roast on sheet pan at 350°F for 10 minutes, set aside. Lightly oil skin of red bell pepper and place in oven on sheet pan. Roast, turning periodically, until soft and the skin is blackened so it can be easily removed. Peel and deseed, cut into thin strips and set aside.
In sauté pan heat small amount of oil and brown sausage, breaking into bite-sized pieces until fully cooked; remove from pan and set aside. In same pan cook onions over medium heat until caramelized, remove pan from heat.
Increase oven temp to 400°F.
Peel and grate potatoes and squash, press grated vegetables between paper towels to remove all moisture. Mix potatoes, squash, 1/2 cup cheddar cheese and 1 egg together until evenly combined. Season to taste with salt and pepper.
Lightly oil sheet pan. Using spatula press crust mixture into pan making a smooth even layer. Brush crust lightly with oil and bake 40 minutes or until golden brown.
While crust is baking, in small sauce pan over medium heat, whisk sugar into sherry vinegar until full dissolved. Add sage leaves and allow to simmer, stirring occasionally until thickened. Once a syrup consistency is reached, remove from heat and remove sage leaves.
To assemble pizza, sprinkle remaining cheddar cheese and crumbled blue cheese evenly over baked crust, repeat with roasted red pepper, caramelized onion, sausage and cherry tomatoes. One at a time, crack remaining eggs into small bowl, being careful not to break the yolk, and gently slide egg on top of pizza. Once all eggs have been placed carefully slide pizza back into oven and bake until eggs have reached desired doneness.
To serve, drizzle pizza evenly with sherry syrup, slice and serve.