INGREDIENTS
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4 teaspoons extra-virgin olive oil, divided
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1 cup thinly sliced shallots, divided
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1 (8-ounce) package presliced cremini mushrooms
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2 tablespoons dry white wine
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1/2 teaspoon freshly ground black pepper, divided
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1/4 teaspoon kosher salt
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8 teaspoons refrigerated pesto
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4 (1 1/2-ounce) slices multigrain bread
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2 ounces grated fresh Parmigiano-Reggiano cheese (about 1/2 cup)
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4 large eggs
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8 (1/4-inch-thick) slices beefsteak tomato
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3 tablespoons chopped fresh basil