Heat oil in a Dutch oven or large pot over medium-high heat. Season pork with salt and pepper, then cook in hot oil until golden brown on all sides, about 7 minutes. Transfer pork to a plate.

Reduce the heat to medium; stir in onion and garlic. Cook and stir until onion has softened and turned translucent, about 5 minutes. Return pork to the pot; stir in chicken broth, green chiles, diced tomatoes with juice, and tomatillo salsa. Season with oregano and ground cloves. Bring to a simmer over medium-high heat, then reduce the heat to medium-low, cover, and simmer for 20 minutes.

After 20 minutes, transfer 2 cups of soup (without any pork pieces) to a blender. Hold down the lid of the blender with a folded kitchen towel, and carefully start the blender, using a few quick pulses to get the soup moving before leaving it on to purée. Purée until smooth, then pour back into the cooking pot. This will create a thicker texture for your chili and will eliminate some of the chunky bits of chiles. Continue to simmer, stirring occasionally, until pork is very tender, at least 35 minutes more.