Heat oil in a Dutch oven over medium-high heat. Cook pork until all sides are golden brown, about 8 minutes. Remove from Dutch oven and set aside.
Reduce heat to medium; add onion and garlic to the Dutch oven. Cook for 4 minutes. Add fresh tomato. Continue cooking, stirring frequently, until onions start to turn translucent and golden, about 4 minutes more.
Return pork to the Dutch oven. Add green chiles, beer, tomatillo salsa, and canned tomatoes. Season with salt, pepper, oregano, and cloves. Bring to a simmer over medium-high heat. Reduce heat to medium low, cover, and simmer for 20 minutes.
Remove 2 1/2 cups of the vegetables from the chili and carefully puree in a blender until smooth. Stir puree back into the chili. Cover and simmer, stirring occasionally, for 10 minutes. Stir in Cheddar cheese. Cover and simmer for 10 minutes more.