Heat the chicken stock in a large pot with an 8-ounce ladle.
In a 4-quart pot, heat 3 tablespoons of the oil and 1 tablespoon of the butter over medium heat. Add the shallot, garlic, red pepper flakes to taste, the thyme leaves and a pinch of salt and cook, stirring, until fragrant, about 1 minute. (Take the pan off the heat if the garlic starts to brown.) Lower the heat to medium-low and cook, stirring occasionally, until the shallot is very tender, about 5 minutes.
Add the rice and 1 tablespoon of the oil to the pot, stirring for about 3 minutes to toast it lightly. Increase the heat to medium, add the wine and cook until most of the wine is gone but the bottom of the pot is not dry. Season the stock with salt if necessary, then add 1 cup of the warm chicken stock and cook, stirring, until the liquid has been absorbed and evaporated. Add another cup stock and increase the heat so that there is a fair amount of bubbles on the surface and cook until the liquid is once again absorbed (this agitation helps release the starch as the rice cooks). Add the remaining 1 tablespoon oil and another cup or so of stock and continue to cook, stirring, until the liquid is absorbed into the rice, adding more stock as needed and stirring. To see if it's time to add more liquid, drag the spoon through the rice; if the liquid doesn't immediately fill in the space, it's time to add more. Continue to cook, adding broth as necessary, until the risotto looks creamy but the rice is still al dente, about 18 minutes.
Take the risotto off the heat. Add the remaining 3 tablespoons butter and the cheese and stir well. At this point, you can add the egg yolks and stir them in until well combined. Serve immediately.