Peel the skin off the garlic. Cut the stem end off the bulb of garlic to reveal the cloves and make them easier to press out.
Wrap the bulb of garlic in foil, then bake at 350 for 20 minutes, turn off the oven and allow them to continue cooking with the residual heat until cool.
The cloves of garlic should be soft and supple. Squeeze out the garlic, mash to a paste and reserve. From here the garlic can be prepared ahead of time.
Rinse the chanterelles under cold water to clean them and allow them to soak up moisture (counter-intuitive but actually a good technique for them).
Warm the chanterelles in a dry pan with the shallots, cooking until the chanterelles have given up their juice and are wilted. Add the olive oil, roasted garlic paste and crushed red pepper flakes and cook for a minute more.
Add the wine and cook down by half, then add the chicken stock.
Meanwhile, cook the pasta in salted boiling water until al dente, then add to the pan along with the butter and herbs and cook for a minute to reduce, toss to combine and coat the noodles with the sauce.
Add a splash of pasta cooking water if the pan gets dry.
Remove the pan from the heat and add half of the cheese. Double check the seasoning for salt and pepper, adjust as needed, then pull the pasta out of the pan with tongs. Twirl the noodles into two warmed pasta bowls. spoon the mushrooms and juices over them, garnish with pecorino or parmesan cheese and serve.
