Heat a large skillet over medium heat. Add oil to pan; swirl to coat. Add shallots and thyme; cook 3 minutes or until lightly browned, stirring occasionally. Reduce heat to low; cook 4 minutes or until shallots are completely tender. Place shallots in a large bowl; leave thyme in pan. Increase heat to medium. Add mushrooms and garlic to pan; cook 5 minutes or until mushrooms are tender, stirring occasionally. Remove thyme sprigs; discard. Add mushroom mixture to shallots in bowl.
Cook fava beans 1 minute in boiling water; drain and place immediately into ice water for 30 seconds. Drain well. Remove outer membranes from beans; discard membranes. Add beans, juice, 1/4 cup parsley leaves, pepper, and salt to mushroom mixture; toss well.
Combine milk, 1 1/2 tablespoons chopped parsley, basil, rind, and cheese in a bowl. Spread 1 1/2 teaspoons cheese mixture over top of each bread slice. Top each bread slice with 1 tablespoon mushroom mixture.