Preheat the Oven and Prepare the Stone: Place a pizza stone on the lowest rack of your oven and preheat the oven to its highest temperature, ideally between 500°F (260°C) and 550°F (287°C). Let the stone heat for at least one hour to ensure even, intense heat that will crisp your crust beautifully.
Prepare the Dough for Stretching: If using refrigerated dough, allow it to rest at room temperature for about 15 minutes to loosen up and become easier to handle. The dough should have visibly risen; if not, keep it covered and let it proof a bit longer at room temperature.
Flour Your Workspace and Flatten Dough: Dust your countertop and hands with flour to prevent sticking. Flip the dough into a bowl of flour to coat it evenly, then place it on your work surface. Press down firmly in the center with your fingers, gradually pushing outward to flatten the dough into a rough 7 to 9-inch (18 to 23 cm) circle, leaving the edges untouched to form the crust rim.
Stretch the Dough to Desired Size: Carefully pick up the dough with floured hands and gently stretch it by letting gravity help, aiming for a 14 to 16-inch (35 to 40 cm) diameter. Take care not to tear or create holes. Lay the stretched dough back on the floured surface.
Transfer Dough to Peel with Semolina Dusting: Sprinkle semolina flour generously on your pizza peel to create a non-stick surface. Gently lift the dough and place it on the peel, making sure both the dough and peel are well-floured to allow smooth sliding later.
Add Toppings in Order: Begin by scattering the fresh mozzarella pieces evenly, then sprinkle the shredded mozzarella. Layer the baby spinach and garlic slices over the cheese. Evenly distribute the crumbled sausage on top. Pour the heavy cream gently over the toppings, then season with a pinch of sea salt.
Bake the Pizza and Add Eggs: Slide the pizza from the peel onto the hot stone in the oven. Bake for 3 minutes, then carefully pull out the oven rack with the stone. Crack the eggs directly onto the center of the pizza, season with salt and pepper, and return the rack to the oven.
Finish Baking and Broil for Crust: Continue baking for up to 7 more minutes, monitoring closely. Once the crust has puffed and cheese bubbles, switch the oven to broil and cook from the top until the crust develops blistered spots and the cheese browns lightly. Keep an eye to avoid burning.
Final Touches and Serve: Remove the pizza from the oven and sprinkle chopped chives and crushed red pepper flakes on top. Drizzle with extra-virgin olive oil and finish with grated hard cheese. Slice and enjoy immediately.