Pat the chicken chunks dry with paper towels—this is crucial for achieving a good sear. Season the dried chicken generously with salt and pepper, tossing to coat evenly. While you're prepping, slice the mushrooms into 1/4-inch pieces, mince the garlic, finely mince the shallot, and roughly chop the spinach. Measure out the white wine, heavy cream, and grated parmesan so everything is ready when you need it.
Heat the avocado oil in a large skillet over medium-high heat until it shimmers. Working in batches if needed to avoid overcrowding, add the seasoned chicken and sear for 6-7 minutes per side until golden brown and cooked through to 165°F. I find that resisting the urge to move the chicken around too much gives you a much better crust. Transfer the cooked chicken to a plate and tent loosely with foil to keep warm.
In the same skillet (don't clean it—those browned bits add flavor), add the sliced mushrooms and minced shallot over medium-high heat. Sauté for about 6-7 minutes, stirring occasionally, until the mushrooms release their moisture and begin to brown. Add the minced garlic and cook for another 30 seconds until fragrant. Then add the chopped spinach and stir constantly for about 1 minute until it wilts completely.
Pour the dry white wine into the skillet, scraping the bottom with a wooden spoon to loosen all those flavorful browned bits. Let the wine reduce slightly for about 1-2 minutes. Reduce the heat to medium-low and pour in the heavy cream, stirring gently to combine. I like to add the Dijon mustard here as it adds a subtle tang that brightens the whole sauce without being obvious.
Slowly sprinkle the freshly grated parmesan into the cream mixture while stirring constantly over medium-low heat. Let it melt completely, stirring for 3-5 minutes, until the sauce is smooth and creamy. Stir in the fresh thyme leaves. Keep the heat low so the cream doesn't break or separate.
Return the cooked chicken from Step 2 to the skillet with the creamy spinach and mushroom sauce. Gently stir to coat the chicken, then let everything warm together over low heat for about 1-2 minutes until the chicken is heated through and reaches 165°F. Taste and adjust seasonings as needed. Serve immediately while the sauce is still creamy and the chicken is tender.