Place oven rack in the upper third of the oven and preheat to 500°F/260°C.
To make dough: (If you are making dough)
Add water to the bowl of a standing mixer and sprinkle yeast over the top. Let sit for 10 minutes. At this point the yeast should be frothy, if it's not, it's likely your yeast has gone bad and you should start again with a new package.
Add 1 ¾ cup flour, salt, and olive oil to the yeast mixture and stir with a spatula until well combined. Place the dough hook on your standing mixer and run for 5-6 minutes, or until the dough is smooth but slightly sticky. If it's too sticky you can add a couple tablespoons of additional flour as it's kneading.
Dump the dough onto a well floured surface (I use a large cutting board) and shape into a ball. Cut the dough into 4 equal sized pieces, dust the top of each ball with flour, and cover with a floured piece of plastic wrap. Make sure you have allowed for enough space for each piece to rise. Place in a warm room and let rise until doubled, about an hour to an hour and a half.
To assemble and cook
Once the dough has doubled you're ready to make your pizza.
Cover a large baking sheet with a sheet of parchment. Flour your hands and then stretch each ball into a 5 inch round, carefully placing each round on the parchment covered baking sheet.
Spread 1 to 1 ½ tablespoons of the jelly/jam on each pizza, leaving a half inch border around the edge. Crumble the goat cheese and top each pizza with 1 oz of cheese, leaving a gap in the middle for the egg. Crack one egg into a small bowl and carefully tilt the egg from the bowl to the center of one of the pizzas. Repeat for the remaining three eggs and pizzas. Sprinkle about half of the scallions over the four pizzas.
Carefully place the baking sheet into the oven and set the time for 8 minutes. After 8 minutes you should monitor your pizza and cook until the egg is cooked to your liking. I like my eggs a little runny, so I cook my breakfast pizzas for exactly 12 minutes.
Remove baking sheet from oven and top with additional scallions. You can season with some salt and pepper if you'd like. Let cool for a few minutes and then enjoy!
Tip: For a nice browned crust, brush the edges of the crust with olive oil before baking.Crust recipe is adapted from Gourmet .