Put the porcinis in a large bowl. If the porcinis are large, tear them into bite-size pieces. Bring the vegetable broth to a boil in a saucepan on the stovetop or in the microwave, and pour it over the porcinis. Cover the bowl with a plate to keep it hot while you prep everything you need. This will soften them and make the recipe go a bit faster.
Preheat a Dutch oven over medium heat. Heat the oil, then sauté the onion and a pinch of salt until translucent, 4 to 7 minutes. Add the garlic and cook until fragrant, about a minute.
Add the sliced cremini mushrooms (not the porcinis yet), celery, thyme, and rosemary and sauté until the mushrooms release their moisture and brown slightly, about 5 minutes.
Add the carrots, stout, tomato paste, remaining 1¼ teaspoons salt, and a lot of freshly ground black pepper and bring to a boil. The liquid should reduce in about 3 minutes. Add the porcinis and vegetable broth, cover, and bring to a full boil for 5 minutes or so, to finish cooking and softening the porcinis.
In a measuring cup, whisk the flour into the cold water with a fork until no lumps are left. Slowly add the slurry to the pot, mixing well as you go. Let the stew thicken for 5 minutes or so. Add the kidney beans, turn off the heat, and cover the pot to keep warm.