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1
In a large pot, bring water to a boil over high heat and salt generously. Cook pasta to al dente, according to package instructions.
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2
In a large pan, cook guanciale over medium heat, until bacon turns opaque but not burnt. Set aside to drain over paper towels. Dispose of bacon grease and wipe clean the pan.
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3
In the pot you used for cooking pasta, melt the butter over medium-low heat. Sautee garlic until golden, about 1 to 2 minutes. Increase the heat to medium, add the chanterelle mushrooms and sautee until juicy (if it is dry, then you may have overcooked them), about 2 to 3 minutes. Season with salt to taste. Add half the Chardonnay wine (1/2 cup), and cook for another 1 to 2 minutes or until the wine reduces. When mushrooms are done, turn heat off but leave mushrooms in the pot, but away from heat.
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4
Back to the other pan (the one used to cook bacon), heat the remaining half of the wine (1/2 cup) over mdium heat until it reaches a boil and is reduced to half, then add the vegetable broth first, followed by the cream. Stir thoroughly. If you want a thicker sauce, add more cream. If you want a thinner sauce, add more broth.
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5
Bring the cooked pasta back in the pot with mushrooms and stir thoroughly. Pour the cream mixture into the pasta and stir until combined.
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6
Add the cooked guanciale and mix well. Season to taste. Sprinkle with chopped parsley.
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7
Over medium heat, pan fry some quail eggs in an oiled skillet until the edges start to curl and turn golden but the yolks still runny.
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8
Remove from pan with a spatula and lay on top of pasta. Serve immediately.