Place the dried mushrooms into the boiling water and set aside until softened, about 20 minutes. Once softened, squeeze excess water from mushrooms and finely chop. Reserve the mushroom-flavored water.

Preheat an outdoor grill for medium-high heat and lightly oil grate.

Season chicken breasts with salt and pepper. Grill chicken breasts until no longer pink in the center, about 6 minutes per side. Once cooked, set aside.

Pour chicken broth into a large pot, and bring to a boil over high heat. Stir in sun-dried tomatoes, tomato paste, and reserved mushroom liquid. Reduce heat to medium-low, and simmer for 15 minutes.

Meanwhile, heat the olive oil in a large skillet over medium heat. Stir in garlic and onion, and cook until the onion has softened and turned translucent, about 5 minutes. Stir in the chopped mushrooms, artichokes, pepper, parsley, lemon juice, and white wine. Bring to a boil over high heat, then reduce heat and simmer 10 minutes; add to the simmering chicken broth.

Slice the grilled chicken breasts into strips and stir into the simmering soup. Sprinkle with Parmesan cheese before serving.