Chop the onion, garlic, bell pepper, and carrot finely and set aside.
Make sure the shrimp are peeled and deveined, ready for cooking.
Warm olive oil in a large pot over medium heat, then add the onion and cook until softened, about 2 to 3 minutes.
Add garlic, bell pepper, and carrot to the pot and cook until the vegetables start to tenderize, around 3 to 4 minutes.
Pour in the diced tomatoes with their juices and the chicken broth; stir to mix and bring to a gentle simmer over medium-high heat.
Sprinkle in chili powder, smoked paprika, cayenne pepper, ground cumin, salt, and pepper; stir well and let the soup gently bubble for 5 to 6 minutes to develop flavors.
Add the shrimp to the simmering soup and cook for 3 to 4 minutes, stirring occasionally, until the shrimp turn pink and are thoroughly opaque—avoid overcooking.
Stir in fresh lime juice to add brightness and a touch of acidity.
Taste the soup and tweak seasoning as preferred by adding extra salt, pepper, or cayenne pepper for more heat.
Serve the soup warm, garnished with chopped cilantro and lime wedges, if desired.
