Cook the fettuccini according to package directions.
Before draining, reserve about ¼ cup / 60 ml (2 fl oz) of the starchy cooking water, then drain the pasta and set it aside.
While the pasta cooks, heat 1 tsp / 5 ml of olive oil in a very large skillet over medium-high heat.
Add the kale and cook, stirring occasionally, until just wilted, about 2 minutes.
Transfer the wilted kale to a separate bowl.
Return the skillet to the heat and add the remaining 2 tsp / 10 ml of olive oil.
Arrange the chanterelle mushrooms in a single layer and let them cook undisturbed for several minutes until they are nicely browned on the bottom.
Once browned, stir in the minced garlic, shallot, and fresh thyme.
Continue to cook, stirring, until the mushrooms are soft and cooked through, about 2 more minutes.
Add the cooked fettuccini and wilted kale back into the skillet with the mushrooms.
Season with sea salt and black pepper and toss everything together to combine.
Stir in the reserved pasta water, a little at a time, until the sauce lightly coats the pasta and reaches your desired consistency.
Serve immediately in large pasta bowls.
Don't overcrowd the mushrooms in the pan!
Cooking them in a single layer without moving them initially is the key to getting a perfect golden-brown sear.