Preheat the broiler. Place the red bell pepper cut side down a large rimmed baking sheet. Broil for 10-15 minutes or until the skin is well-charred. Check the peppers after about 8 minutes and rotate if some are charring faster than others.
Place the peppers in a bowl and cover for 5 minutes. Once cool enough to handle, remove from the bowl and peel off the blackened skin. Coarsely chop -- you will have about 2 cups of roasted bell peppers.
Heat 1 tablespoon olive oil in a skillet over medium heat. Add the onion and cook for 5 minutes or until softened. Add the garlic, smoked paprika cayenne pepper and saute for 30 seconds.
Add the vegetable stock, 1 1/2 cups of the roasted red bell peppers (reserving half a cup) and kosher salt and scrape up the browned bits from the bottom of the pan. Stir well and simmer for 5 minutes.
Place the mixture into a blender and place the lid on without the insert in order to release steam. Process until smooth and set aside.
Wipe out the skillet and heat the remaining 1 tablespoon olive oil over medium heat. Add the mushrooms and saute for 5 minutes or until the liquid has evaporated and the mushrooms have softened. Add the reserved 1/2 cup roasted red peppers, spinach and pinch salt and cook 2-3 minutes longer or until wilted.
Cook the pasta according to package instructions, reserving about 1/3 cup of cooking liquid. Drain the pasta well and add to the skillet with the mushroom mixture. Add the desired amount of reserved pasta water and enough of the sauce to coat (you'll have some leftover) and heat on low until warm if necessary.
Remove from heat and stir in the goat cheese. Serve topped with toasted walnuts and enjoy!