In a large pot or Dutch oven over medium heat, add olive oil to heat.
Add onion and red bell pepper to the pot. Cook 5–6 minutes until softened.
Add garlic and cook 1 minute until fragrant.
Stir in cumin, chili powder, smoked paprika, and cayenne if using, toasting for 30 seconds until fragrant.
Pour in the broth, scraping up any browned bits. Add sweet potatoes.
Bring to a boil, then reduce heat and simmer 15–20 minutes, until sweet potatoes are fork-tender.
While the soup simmers, whisk the cornstarch into the whole milk in a small bowl or measuring cup until fully dissolved, with no lumps.
Add black beans and corn, then pour in the cornstarch-milk mixture. Return to a simmer and cook 3–4 minutes, stirring occasionally, until the chowder thickens slightly.
Remove the pot from heat. In a small bowl, whisk a ladle of the hot chowder into the Greek yogurt to temper it, then stir the mixture back into the pot. Stir in the lime juice, cilantro, salt, and pepper.
Taste and adjust seasoning.
Top with extra fresh cilantro before serving.