Bring 4 liters of water and 1 tablespoon of salt to a rolling boil in a large stockpot. Submerge tagliatelle and cook until al dente according to package timing. Reserve 125ml of starchy pasta water before draining.
Season the chicken strips with salt and black pepper. In a large high-sided skillet, heat 1.5 tablespoons of olive oil over medium-high heat. Sear the chicken for 6-8 minutes until golden and internal temperature reaches 74°C (165°F). Transfer chicken to a warm plate and set aside.
In the same skillet, melt the butter with the remaining 1.5 tablespoons of olive oil. Add the sliced mushrooms and sauté for 8-10 minutes without stirring frequently to allow for Maillard browning.
Introduce the diced onions to the mushrooms and cook for 3 minutes until translucent. Add minced garlic and cook for an additional 60 seconds until fragrant.
Deglaze the skillet with the dry white wine, using a wooden spatula to scrape the fond from the bottom of the pan. Simmer until the liquid has reduced by 50%.
Pour in the heavy cream and stir in the dried oregano and thyme. Maintain a gentle simmer for 4-5 minutes until the sauce coats the back of a spoon.
Reduce the heat to low and whisk in the grated Parmesan cheese until the sauce is smooth and emulsified.
Incorporate the seared chicken and baby spinach into the sauce. Stir for 1-2 minutes until the spinach is just wilted.
Add the drained tagliatelle to the skillet. Toss thoroughly to coat, adding the reserved pasta water in small increments if the sauce requires thinning for optimal adherence.
Adjust seasoning with salt and pepper. Garnish with fresh parsley and serve immediately.