Heat coconut oil in a stockpot or large saucepan over medium-high heat; cook and stir onion, garlic, paprika, garlic salt, cayenne pepper, and cumin until onion is translucent, about 4 minutes. Add chicken broth, ham, and corn; bring to a boil.

Reduce heat to medium-low and stir pumpkin and coconut milk into broth mixture. Simmer soup, stirring occasionally, until heated through, about 10 minutes; season with salt and pepper.