In a shallow bowl, combine milk and wine. Dip both sides of bread in milk mixture; squeeze gently to remove excess liquid. Layer bread slices in a greased 13x9-in. baking dish.
Sprinkle with basil and parsley; drizzle with oil. Layer with half the cheese, half the prosciutto, and tomatoes; drizzle with half the pesto. Top with remaining cheese, prosciutto and pesto.
In a small bowl, whisk eggs, cream, salt and pepper until blended; pour over top. Refrigerate, covered, several hours or overnight.
Preheat oven to 350°. Remove strata from refrigerator while oven heats. Bake, uncovered, until top is golden brown and a knife inserted in center comes out clean, 50-60 minutes. Let stand 5-10 minutes before serving.
