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Finely mince 4 garlic cloves and place in a medium bowl. Smash 4 garlic cloves with the flat side of a knife and set aside. Thinly slice remaining 4 cloves of garlic and set aside.
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Place shrimp in bowl with minced garlic; add 3 tablespoons olive oil, salt and baking soda; toss well and set aside.
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Pour remaining 1/4 cup + 1 tablespoon olive oil in a large skillet along with smashed garlic cloves and dried chili pepper. Heat on medium-low until garlic is pale golden brown, turning garlic cloves and chili pepper over to brown both sides and pressing down both to release flavor. Remove garlic cloves and chili pepper; set aside as garnish.
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Turn heat up to medium; add sliced garlic and cook until pale golden brown, about a minute. Add shrimp and spread in a single layer. Cook until just cooked through, about 2 minutes. Add sherry vinegar and parsley, and toss to combine. Garnish with browned garlic cloves and chili pepper. Serve immediately.