In a pot, add potato to water or stock and boil until potato is just tender. Once tender, remove from heat.
Meanwhile, in a heavy skillet, sauté onion and garlic until soft (approximately 8 minutes) on medium heat. Add carrots and celery to onion mixture and cook until they start to soften (on my stove, another 6 minutes). Add mushrooms, zucchini and dried herbs, and cook until they start to soften. This two-step process is to avoid over-cooking the more tender components of the soup into a mush.
Remove from heat. Add contents to the potato/stock pot, simmer for another 20 minutes to mix flavors together.
Note: You can stop at this point if you are planning to serve the soup later on the in day. It will keep fine in the fridge or for a few hours on the stovetop if you used water.
Fifteen minutes before serving the soup, bring back to a simmer. Add wine and peas, and simmer for 15 minutes. Season to taste with salt and pepper, which will depend on what you used as your liquid. Commercial stock will be pre-salted. I use 1/2 teaspoon sea salt to season mine when I use water.
Serve in lovely, mismatched bowls that you inherited from your parents, with warm bread, cheese, butter and the rest of the wine you bought. If you can find it, sit at the table instead of the floor. You are all grown up, after all.