Crisp the bacon. Add chopped bacon to a heavy pot over medium heat.
Cook until the fat renders and the bacon turns crisp, 6–8 minutes. Transfer bacon to a plate, leaving 1–2 tablespoons of fat in the pot. If there’s less, add the butter.
Sauté the aromatics. Add the diced onion and a pinch of salt.
Cook 3–4 minutes until translucent. Stir in the garlic and cook 30 seconds, just until fragrant.
Brown the mushrooms. Add the sliced mushrooms and thyme. Cook, stirring occasionally, until mushrooms release their moisture and start to brown, 7–10 minutes.
Don’t rush this step; color equals flavor.
Season the base. Stir in smoked paprika (if using), a few grinds of black pepper, and taste for salt. The bacon and broth add salt, so season lightly for now.
Deglaze and simmer. Pour in the broth, scraping up any browned bits. Bring to a gentle simmer and cook 8–10 minutes to marry the flavors.
If adding greens, stir them in now so they soften.
Melt in the cream cheese. Reduce heat to low. Whisk in the cream cheese a few cubes at a time until completely smooth. This gives the chowder body without flour.
Add the cream. Stir in the heavy cream and warm through.
Do not boil after adding dairy; keep it just below a simmer to prevent curdling.
Brighten and balance. Stir in the apple cider vinegar or lemon juice. Taste and adjust salt, pepper, and acidity. The splash of acid keeps the chowder from tasting flat.
Finish and serve. Return the bacon to the pot, reserving a little for garnish if you like.
Ladle into bowls and top with parsley (and Parmesan, if using). Serve hot.