Cook the rice according to package directions, adding a quarter of the chopped garlic to the water.
In a large skillet, simmer 2 inches of water. Crack the eggs into the water, spacing them apart. Simmer until the whites are set but the yolks are still runny, 3 to 4 minutes. Using a slotted spoon, transfer the poached eggs to a bowl.
In a large skillet, heat 1 tbsp. oil over medium-high. Add the shrimp; stir-fry until opaque in the center, about 3 minutes. Using a slotted spoon, transfer to a plate; drizzle with the lime juice.
In the same skillet, heat the remaining 1 tbsp. oil. Add the carrot and onion and stir-fry until the onion begins to brown, about 4 minutes. Add the remaining garlic and stir-fry until fragrant, about 30 seconds. Add the rice, shrimp and any juices on the plate, half the cilantro and 1 tsp. hot sauce; stir-fry until combined, about 1 minute.
Divide the stir-fry among bowls. Top each with an egg, some shredded cabbage and the remaining cilantro. Serve with the lime wedges and hot sauce.