Preheat the broiler. Coarsely chop tomatoes and garlic. Place in food processor along with artichoke hearts, parsley, walnuts, lemon juice and zest, ¼ cup of olive oil, Parmesan, salt, and pepper. Pulse until combined but still chunky.
Place the slices of bread on a cookie sheet and broil until golden on both sides. Lightly brush slices with remaining 1 teaspoon of olive oil. Spread tomato-artichoke mixture on top and serve.