Heat oven to 475 F.
Using a small knife, slice the ancho chiles in half lengthwise and remove stem and seeds. Place the chiles in a medium bowl and fully cover with hot water. Soak for 10 to 15 minutes, until the chiles are soft. Using a fork or tongs, remove the chiles from water and place in food processor with butter and thyme leaves. Blend on high until well-combined. Remove the ancho chile butter mixture from food processor and set aside in a small bowl.
To roast the peppers using a gas range, turn one burner to medium high. Place the poblano peppers directly on the burner and roast, turning occasionally with tongs, until the peppers are charred all over and soft but not mushy, approximately 7 minutes. Alternatively, place the peppers on a baking sheet and cook under the broiler turning several times until charred all over, about 10 minutes total. Transfer the roasted poblano peppers to a mixing bowl and cover tightly with plastic wrap. Let them steam for 10 minutes, then remove from bowl. Peel the charred skin from the peppers, slice lengthwise, remove the seeds, and then finely chop.
Cook the grits according to package instructions. Once cooked, keep warm and stir occasionally.
Line a baking sheet with aluminum foil. Spread grape bunches evenly on the baking sheet and drizzle with balsamic vinegar; use hands to lightly toss so all bunches are evenly coated. Roast for approximately 12 to 15 minutes, until the grapes are browned but still plump (note not a lot of liquid should be visible on the baking sheet). Remove from oven and set aside.
Rub both sides of each pork chop with olive oil and season liberally with salt and pepper.
Heat a grill or cast – iron pan to medium heat. Using tongs, carefully place each pork chop in the pan, working in batches if necessary. Sear the pork until golden brown on one side, approximately 6 to 8 minutes, then flip and cook for an additional 4 to 6 minutes. Using an instant-read meat thermometer, check that the temperature in the center of each pork chop reads 140 F, then remove pork chops from grill/pan and let rest for at least 5 minutes.
While pork is resting, finish the grits: Over low-medium heat, slowly add the half-and-half, cheese, and chopped, roasted peppers to the grits, stirring constantly to avoid clumping, until the cheese is melted, approximately 2 to 3 minutes. Season with salt to taste.
Serve the pork chops with a dollop of ancho-chile butter on top and the poblano-cheese grits on the side, topped with a bunch or two of the roasted grapes.