Preheat oven to 400F.
To make the pesto:
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Using a Bump and Grind or another large mortar and pestle, smash the garlic into a coarse puree.
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Add 1 1/2 bunches of basil and pound until it is coarsely chopped. Mix in the grated Parmesan cheese.
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Add 1/3 cup of pine nuts and smash to break them up.
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Slowly mix in 1/4 cup of olive oil. Season the pesto to taste with salt and pepper. Set it aside.
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Heat 1 tablespoon of oil in a large ovenproof sauté pan over high heat.
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Sprinkle the chicken breasts generously with salt and pepper. Cook the chicken breasts just until golden brown but not yet cooked through, about 2 minutes per side.
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Remove the pan from the heat. Spread the pesto over the top of the chicken breasts.
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Transfer the pan to the oven and bake until the chicken is just cooked through, about 8 minutes.