Heat the chicken stock in a pot on the stove until steamy / simmering, but not boiling. Reduce the heat to low and keep warm.
Heat a large cast iron skillet, or other oven-safe skillet, on the stovetop over medium heat.
Add the chopped bacon to the skillet and cook it about halfway, 3-4 minutes.
Add the diced onion to the skillet and continue to cook with the bacon until translucent, about 2 minutes. If the onion starts to brown at all, reduce the heat.
Add the Arborio rice to the skillet and cook until the grains of rice are translucent around the edges, about 2-3 minutes. Stir the rice occasionally as it cooks.
Add the dry white wine to the skillet and continue to cook the rice until the wine is completely absorbed, about 3-4 minutes. Stir the rice occasionally as it cooks.
Add one ladle of hot chicken stock to the skillet. Cook the rice, stirring occasionally, until the stock is pretty much completely absorbed. Continue to repeat this process—adding one ladle of hot chicken stock and cooking until it's absorbed into the rice—until the rice is cooked al dente, about 30 minutes. You may not use all of the chicken stock! I begin to test my rice for doneness when I’ve used 3 cups of chicken stock.
When the rice is cooked to your liking, remove the skillet from the heat. Add the Parmesan cheese, butter, and chopped thyme. Stir everything together until well combined, and the cheese and butter have melted throughout the rice.
Using the back of a soup spoon, make four wells in the top of the rice. Crack one egg into each well. Carefully place the skillet into the preheated oven. Bake the risotto for 10 to 12 minutes, or until eggs are cooked to your desired doneness. Carefully remove the skillet from the oven. Top the risotto with more Parmesan cheese and a sprinkle of fresh thyme before serving hot.
To Make Breakfast Risotto Ahead Of Time - Make the risotto using the instructions as listed to the point where you add the butter and Parmesan. After you stir the butter and cheese into the rice to combine, cool the rice and store it in an airtight container in the refrigerator overnight. The next morning preheat the oven to 400ºF. Place the rice in an oven-safe skillet or dish and bake until warmed through, about 15-20 minutes. Carefully remove warmed rice from oven and proceed with the recipe as written.