Heat 3 tablespoons butter with 1 tablespoon olive oil in a large stockpot over high heat. Add the wild mushrooms and cook until the mushrooms are golden brown and their liquid has evaporated, about 8 to 10 minutes. Transfer the mushrooms to a bowl.
Heat 1 tablespoon butter with 1 tablespoon oil in a medium saucepan over medium-high heat. Add the onion and cook until soft. Add the cremini mushrooms and cook until golden brown, about 4 to 5 minutes. Sprinkle flour over mushrooms and cook for 2 minutes. Add the stock and porcini powder and cook for 20 minutes. Season, to taste, with salt and pepper. Strain the stock through a strainer into the stockpot that you sauteed the wild mushrooms in and discard the onion and mushrooms.
Cook stock over medium heat until thickened slightly and then stir in the sauteed wild mushrooms and cook for 15 minutes. Season, to taste, with salt and pepper.
While the soup is cooking, heat the canola oil in a high sided saute pan over high heat until the oil begins to shimmer. Carefully add the ham, in batches, and cook until crispy, about 45 seconds to 1 minute. Drain on a plate lined with paper towels.
Ladle the soup into bowls, add a handful of arugula, top with a slice of the crispy ham, and drizzle with a teaspoon of white truffle oil.
Rich Chicken Stock:
Preheat oven to 450 degrees F.
Combine chicken bones, onions, celery, and carrots in a large roasting pan; toss with oil and season lightly with salt and pepper. Roast until the bones and vegetables are a rich golden brown, about 30 to 40 minutes.
Transfer the bones and vegetables to a large stockpot, add 12 cups cold water, and the remaining ingredients and bring to a boil over high heat. Reduce the heat to medium and simmer for 4 hours, skimming the scum that rises to the top with a ladle every 20 minutes. Remove from the heat and strain through a mesh strainer into a clean pot. Place back on the stove over high heat and cook until reduced by half. Use immediately or let cool to room temperature, cover, and refrigerate or freeze until ready to use.