Position a rack in the center of the oven and heat the oven to 400°F.
Whisk together the garlic and 2 Tbs. of the oil in a small bowl. Brush onto 1 side of the baguette slices and arrange, oiled side up, on a rimmed baking sheet. Arrange overlapping slices of tomato on each, season with salt and pepper, and top with the cheese. Bake until the bottom side is browned and the cheese is melted, 12 to 15 minutes. Set aside.
In a medium bowl, whisk the eggs, basil, and a pinch of salt until blended but not foamy.
Heat the remaining 2 Tbs. oil in a 12-inch nonstick skillet over medium-low heat. Add the eggs and cook, stirring with a silicone spatula, until the eggs are beginning to set. Add the salami, separating the strips as you add them. Continue to cook, stirring, until the eggs are softly set, 4 to 5 minutes total. Season to taste with salt and pepper and serve with the tomato toasts.
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