For dried porcini: Soak the mushrooms (1 ½ oz/45 g) in warm water (2 cups/480 ml) for 20 to 30 minutes. Lift them out, squeeze gently, and strain the liquid through a coffee filter. Save the liquid.
Wipe the fresh porcini (1 lb/450 g) clean without rinsing and cut into thick pieces (skip this for dried ones). Finely chop the onion (1 large) and mince the garlic (3 cloves).
Bring water (4 cups/1 l) to a rolling boil in a medium pot. If using dried porcini, use the strained soaking liquid, topped up with fresh water. Rinse the groats (1 ¼ cups/220 g) in a sieve, add to the pot, and simmer for 12 minutes, until tender with a slight chew. Drain.
Meanwhile, melt the butter (3 ½ tbsp/50 g) in a wide, deep pan over medium heat. Cook the onion until glassy with a hint of color.
Raise the heat to medium-high. Add the mushrooms and garlic. If they cling to the pan, loosen them with water or white wine (1 tbsp).
Sauté for about 5 minutes, stirring constantly, until the mushrooms are tender and reduced. Season with salt (2 tsp) and black pepper (1 tsp).
Stir in the heavy cream (1 cup/250 ml), dried marjoram (1 tsp), and dried thyme (1 tsp). Cook briefly until silky.
Add the drained groats and most of the parsley (½ cup/30 g, chopped). Toss, cover, and let stand for 1 to 2 minutes to absorb the sauce.
Serve hot, topped with the remaining parsley.