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1
In a large Dutch oven or stock pot, heat 2 tablespoons oil over medium. When it starts to shimmer add chicken wings. Cook until well-browned on all sides, about 10 minutes. Remove to large plate. Add the bones to the pot, and cook until browned over most of their surface, another 12 to 15 minutes. Remove to plate with the chicken wings.
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2
If the pot seems dry, add 1 tablespoon oil. Add the garlic and fennel stems. Saute, stirring occasionally, until translucent and softened, about 5 to 6 minutes. Add the vermouth, and cook, scraping the bottom to remove any browned bits that have accumulated, until most of the liquid has evaporated. Reduce heat to low, and add the wings and bones back to the pot. Cover, and cook for 15 to 20 minutes, until the wings have released their juices.
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3
Add 8 cups water, garlic, and bay leaves. If the bones and wings are not mostly covered, add 2 cups of water. Increase heat to high until broth reaches a simmer. Reduce heat to low and cover. Maintain a very gentle simmer for at least 6 hours or overnight.
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4
Add remaining ingredients, re-cover, and simmer an additional 30 or more minutes. After about 30 minutes start tasting every 10 to 15 minutes until you are happy with the flavor the aromatics have added. (I stopped at about 60 minutes). Salt to taste.
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5
Strain stock into large bowl. I used a colander to get the large bits, then a straining bag to collect the small stuff. Transfer back into the (cleaned) pot or a wide shallow container, to help increase the surface area for cooling. Once cooled to room temperature, transfer to the fridge. When the fat solidifies, skim it off the surface and portion out the stock into suitable storage containers. Store any that won't be used within a few days in the freezer.
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6
Heat as much or as little as desired to fill a mug or thermos. Sip and feel better!
