Peel the zucchini (or not, I peeled mine just for the look and munched on the peels while I was cooking) and cut them into wide julienne strips with a mandolin. Set aside. (I used the wider setting of my mandolin to create Fettuccine-like “noodles”, but you could also do finer noodles with the thinner setting or you could also use a vegetable spiralizer.)
Add onion, garlic, salt and pepper to a medium saucepan. Cook over medium heat for one or two minutes, until fragrant and slightly softened.
Throw the cauliflower in and continue cooking for a minute or two.
Add chicken stock, cover and bring to the boil; lower heat and continue cooking until the cauliflower is tender, about 5-7 minutes.
Meanwhile, cook the mushrooms in a large skillet until nice and golden. Add chicken and continue cooking until heated through; Reserve.
Ladle the cauliflower mixture into your blender; add Dijon mustard, nutritional yeast, balsamic vinegar and lime juice and process on high speed until super smooth and silky in consistency. Throw in capers and pulse 2-3 times just to mix them in and break them down a little. Pour that cauliflower mixture over the reserved chicken and mushrooms and bring to a simmer over low-medium heat.
Divide the julienned zucchini between serving plates and ladle the chicken sauce on top.
The heat from the sauce alone will soften the zucchini some, but it you want your "pasta" to be even softer still, you can also add the zucchini to the pan, stir until well coated and cook over low heat for a minute or two.