On baking sheet broil eggplant and bell pepper 3 inches from heat source, turning frequently, until charred on all sides; transfer to brown paper bag and let stand until cool enough to handle, 15 to 20 minutes. Peel and dice eggplant; transfer to medium bowl. Peel pepper; remove and discard stem end and seeds. Cut pepper into thin strips and add to eggplant; add artichoke hearts to bowl and set aside.
Spray 9-inch skillet with nonstick cooking spray and heat over medium-high heat; add mushrooms and cook, stirring occasionally, until just cooked through, 1 to 2 minutes. Add to eggplant mixture. In small bowl combine remaining ingredients, mixing well; pour over vegetable mixture and toss to coat. Cover with plastic wrap and let marinate for at least 30 minutes. Serving for 4.