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Split open the Hatch Chiles and drizzle with olive oil.
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Grill the chiles until the skin is charred.
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Transfer to a bowl and cover with plastic wrap for a few minutes until the skin releases, and it’s easy to peel.
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Once removed, stuff them with the Oaxaca cheese (you can also substitute with Mozzarella cheese) and put them back on the grill until the cheese melt.
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Combine diced avocados, tomatoes, and half of the chopped garlic, season with salt and pepper. Set aside.
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In a large sauté pan, add olive oil, shallots, and the rest of the garlic and tomatoes. Cook for about 5 minutes. Add shrimp, season with salt and pepper, and sauté until pink.
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Put the grilled Hatch Chiles onto a plate and top it with the shrimp mixture, layered with the avocado mixture, lime juice, and chopped cilantro.
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Done. Ready to serve.