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1
Heat grill to medium-high, or heat a grill pan over medium-high heat, until hot but not smoking. Rub beef with 1/2 tablespoon oil and generously season with salt and pepper. Grill, turning every 5 minutes, about 25 minutes for medium-rare.
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2
Meanwhile, thinly slice 1 garlic clove. In a 12 inch skillet, heat 1-1/2 tablespoons over medium-high heat. Add bell peppers, onion, sliced garlic, and a generous pinch of salt and pepper; cook, stiring frequently, until vegetables are tender, about 8 minutes. Transfer mixture to a large bowl.
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3
Return skillet to medium-high heat; add remaining 1-1/2 tablespoon oil and heat until oil is hot but not smoking. Add eggplant and a generous pinch of salt and pepper; cook, stiring frequently, until eggplant is tender, 10-12 minutes, Add tomatoes and toss to combine; cook for 1 minute more. Transfer mixture to bowl with peppers and onion. Add sliced basil leaves; stir to combine. Adjust seasoning.
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4
Remove beef from grill and let stand for 10 minutes.
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5
Meanwhile, in a blender, puree remaining 1/2 cup oil, remaining garlic clove, whole basil leaves, parsley, and 1/2 teaspoon fine sea salt until smooth.
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6
Spread 2 tablespoons pesto over rested beef. Serve beef sliced, with remaining pesto vegetables and coarse sea salt for seasoning.