Warm the oil in a medium-large heavy-bottomed pot or Dutch oven over medium heat. Add the chopped onion and a pinch of salt. Cook 4–5 minutes, stirring often, until the onion is translucent and just starting to turn golden around the edges.

Stir in the minced garlic and sliced mushrooms. Cook 6–8 minutes, letting the mushrooms release their liquid and then begin to brown. Stir occasionally but not constantly so they can caramelize slightly.

Add the thyme, oregano, smoked paprika (if using), remaining salt, and black pepper. Stir to coat the vegetables and let the spices toast for 30–60 seconds, until fragrant.

Add the diced potatoes and bay leaf. Pour in 3 cups of vegetable broth, or just enough to cover the potatoes. Bring to a gentle boil, then reduce the heat and simmer 10–12 minutes, or until the potatoes are fork-tender but not falling apart.

Scoop about 1 cup of the cooked potatoes plus some broth and mushrooms into a blender. Add the raw cashews and plant milk. Blend until completely smooth and creamy, starting on low and increasing to high. (Alternatively, use an immersion blender to partially blend the soup directly in the pot.)

Pour the creamy mixture back into the pot and stir well. Simmer another 3–5 minutes to let the flavors meld. If the soup is too thick, add a splash of broth or water; if it’s too thin, simmer uncovered for a few more minutes.

Turn off the heat and stir in the lemon juice. Taste and adjust with more salt, pepper, or lemon as needed until the flavor is balanced and bright.

Remove the bay leaf. Ladle the soup into bowls and top with fresh thyme leaves or chopped parsley and extra black pepper, if desired. Serve hot with your favorite crusty bread or sides.