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1
Chop up the onions. Put them in a large wok with a couple tablespoons olive oil. Cook on high for a few minutes until the onions are hot and starting to become translucent, then turn down the heat to medium low. As the rest of the steps progress, you'll need to remember to stir the onions every 8 minutes to keep them from burning. The onions will take a long time to reach the desired golden-brown color.
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2
Peel the outer, papery skin off two heads of garlic, but leave the skin that covers the cloves. Slice the tips of the cloves off the top, exposing each clove and leaving a flat top. Save the tips, which you'll toss into the onions when they're almost finished cooking. Drizzle the heads with olive oil, wrap them in foil, and place them in a 400 degree Fahrenheit oven for 40 minutes.
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3
Quarter the button mushrooms from top to bottom. Each mushroom piece should have part of the head and part of the stem.
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4
When the onions are approaching done (not the rich brown of fully caramelized onions, but getting there) add the mushrooms and leftover garlic clove tips to the cooking onions. Stir everything together and cook until the mushrooms are looking sauteed.
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5
With the onions, mushrooms, and garlic still in the pan, turn the heat up to high and add the wines. Scrape the bottom of the pan to make sure the sugars from the onions are released and integrated into the liquid.
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6
Add the chicken base. You can add a bit more to taste if you want. We're looking for a nice strong chicken flavor, but be careful of over-salting. At this point the sauce should taste pretty good.
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7
Cut up the raw chicken into scallop-sized pieces and put them in the pan with everything else. There's also no harm in using some leftover cooked chicken as well, as long as it doesn't have any incompatible flavorings. Let the chicken cook through.
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8
The next step is to add the pasta into the same pan. Before you do, make sure the amount of liquid is right. It takes some experience to eyeball it, but the idea is to just barely (or not quite) cover the noodles once they're in the pan. It's better to start with too little liquid than too much because you can always add some boiling water from a teapot after you've added the pasta, but you don't want to be reducing after the pasta is cooked, because the pasta will overcook and get mushy. As it cooks, the pasta takes on the flavor of the sauce and releases starches that thicken the sauce at the same time.
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9
Monitor the pasta as it cooks. When it's just reaching the perfect al dente, turn off the heat and stir in the heavy cream and grated Parmesan cheese. Cut up the butter into pieces and stir them into the sauce. Squeeze out the roasted garlic (don't burn yourself!), mash it up, and stir it in as well. Add freshly cracked black pepper to taste and serve.
