How to Make It
Preheat the oven to 375°. In a large skillet, melt the butter over moderate heat until lightly browned. Add the minced garlic and cook until golden and fragrant. Stir in the chopped thyme, diced bread and Parmigiano-Reggiano cheese. Season with salt and pepper. Spread the croutons on a large baking sheet and toast in the oven for about 10 minutes, stirring occasionally, until crisp.
In a large skillet, heat 2 tablespoons of the olive oil over moderate heat until just smoking. Add the shallots and thyme and cook, stirring, until the shallots begin to brown, about 5 minutes. Add the shiitakes and cook until tender and golden brown around the edges, about 5 minutes. Season the shiitakes with salt and pepper.
In a large bowl, mix the croutons with the tomato sauce, diced tomatoes, basil, red onion, red wine vinegar, the cooked shiitakes and the remaining 2 tablespoons of olive oil. Season with salt and pepper. Mound the panzanella on plates and garnish with the baby greens, cherry tomatoes and the Parmigiano-Reggiano.