In a large pot, heat the olive oil or vegan butter over medium heat. Add the diced onion and sauté until translucent, about 5 minutes.
Stir in the minced garlic and cook for an additional minute until fragrant.
Add the chopped hearts of palm and cook for another 2-3 minutes, allowing them to absorb the flavors.
Sprinkle the flour over the mixture, stirring to coat the vegetables evenly. Cook for 1-2 minutes to remove the raw flour taste.
Gradually pour in the vegetable broth, stirring constantly to avoid lumps. Bring the mixture to a simmer.
Once simmering, add the plant-based milk, coconut milk, nutritional yeast, dried thyme, Old Bay seasoning, smoked paprika, and season with salt and black pepper to taste. Stir well to combine.
Let the chowder simmer for about 15 minutes, stirring occasionally, until it thickens slightly.
Taste and adjust seasoning if necessary. Serve hot, garnished with fresh parsley.