In a large (10-inch) skillet, heat the oil over medium. Add the garlic cloves and adjust the heat so that they are sizzling very gently. Cook until they are browned around the edges, about 5 minutes. They should have a nice amount of color, but letting them brown too much will turn them bitter.
Scoop the garlic and oil into a blender or food processor and add the lime juice and salt. Pulse until the garlic is chopped into bits no bigger than about 1/8 inch. Pour into a storage container and let the garlic settle to the bottom.
Scoop the sweet potato cubes into a microwave-safe bowl, splash on a couple of tablespoons of water, cover (if using plastic wrap, poke a few holes), then microwave for about 3 ½ minutes on high.
Set a very large (12-inch) skillet over medium-high heat and add several tablespoons of the oil from on top of your garlic preparation. Drain the sweet potatoes and add to the skillet. Cook, stirring regularly, until they are beginning to brown. Nestle in the shrimp, making sure that each piece is touching the bottom of the pan. Cook for a couple of minutes, then turn the shrimp and cook for a minute or two longer on the other side. Stir in some of garlic solids from your mojo preparation, along with the chipotle. Taste and season with additional salt if necessary, then scoop into a serving bowl and sprinkle with cilantro leaves. Refrigerate the remaining garlic mojo in a tightly sealed container for later.