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1
Turn a gas grill to high or ignite charcoal. When the grill is hot, for both gas and charcoal grills, clean your grill rack. Decrease the temperature to medium-high (on a gas grill only), and brush or wipe a little olive oil on the grill rack.
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2
Halve, peel and pit the avocados. Put the flesh in a bowl and give it a little squeeze of fresh lemon juice to keep it from going brown.
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3
Drizzle the avocado halves with about 1 Tb. of the olive oil and sprinkle with salt and pepper.
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4
Peel the mangoes and have them ready for the grill. Halve the red onion lengthwise into 2 equal pieces (save one piece for another use).
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5
Cut the remaining piece crosswise into thin half-moons. Place the onion slices in a small bowl and pour over the reserved 1Tb. of fresh lemon juice. Toss and set aside. With tongs, place the peeled avocados and mangoes on the grill rack.
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6
Grill until you see some grill marks, about 1 to 2 minutes, and then turn them over and grill for another minute. Take avocados and mangoes off the grill and set aside to cool.
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7
Preheat a 10-inch saute pan at the stove or a cast-iron pan on the grill. Add 1/4 cup of olive oil to the pan, add the minced garlic, and saute until it begins to show some color. Add the basil and saute until wilted. Transfer to a large glass or ceramic bowl and allow to cool.
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8
With a fork, mash the grilled avocado into the basil mixture. Add the sour cream or creme fraiche and stir. Add the Parmesan and stir. Dice the grilled mango after cutting away and discarding the pits. Gently stir in the mango and the red onion with its lemon juice.
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9
Taste and add more sea salt and pepper if you like. Serve or cover with plastic wrap, smoothing it across the top of the guacamole to keep it from discoloring.
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10
Refrigerate until you're ready to serve. This is best served on the same day it's made.
