If you absolutely must use bloody mary mix for some reason
Brown up your beef, saute up some diced onions and crushed garlic and the peppers
Add it all to a pot, add the bloody Mary mix
Season with some cumin, and (if needed, some bloody Mary mixes can be pretty heavily seasoned) salt, pepper, garlic & onion powder, chilli powder, maybe some herbs like cilantro, oregano, maybe basil
Maybe a bit of flour to help thicken it, otherwise you’re gonna need to be very judicious about how much mix you use or it’s gonna take forever and risk the flavor getting weird trying to reduce it down and concentrating the seasoning in the mix.
If it’s coming out a bit too tangy and acidic, a bit of sugar or maybe brown sugar can help cut that
If you can, consider using some fresh or canned tomatoes, or even plain tomato sauce, that’ll probably get you a better texture, but I suspect that if that were an option you could, should, and probably would skip the bloody Mary mix
I’d also maybe consider adding some bell peppers to the mix to make it a little chunkier. Maybe some corn.
Maybe some bacon, chorizo, some diced meat in addition to the ground, etc.
I like to add a beer, but starting with bloody Mary mix that’s probably gonna thin things out a bit too much. Wine and stock would be other options but with the same problem.
End of the day, chili is a stew, and the origin of stews is pretty much just throwing whatever you have in a pot and letting it simmer, there’s not too much to it.
If you absolutely must use bloody mary mix for some reason
Brown up your beef, saute up some diced onions and crushed garlic and the peppers
Add it all to a pot, add the bloody Mary mix
Season with some cumin, and (if needed, some bloody Mary mixes can be pretty heavily seasoned) salt, pepper, garlic & onion powder, chilli powder, maybe some herbs like cilantro, oregano, maybe basil
Maybe a bit of flour to help thicken it, otherwise you’re gonna need to be very judicious about how much mix you use or it’s gonna take forever and risk the flavor getting weird trying to reduce it down and concentrating the seasoning in the mix.
If it’s coming out a bit too tangy and acidic, a bit of sugar or maybe brown sugar can help cut that
If you can, consider using some fresh or canned tomatoes, or even plain tomato sauce, that’ll probably get you a better texture, but I suspect that if that were an option you could, should, and probably would skip the bloody Mary mix
I’d also maybe consider adding some bell peppers to the mix to make it a little chunkier. Maybe some corn.
Maybe some bacon, chorizo, some diced meat in addition to the ground, etc.
I like to add a beer, but starting with bloody Mary mix that’s probably gonna thin things out a bit too much. Wine and stock would be other options but with the same problem.
End of the day, chili is a stew, and the origin of stews is pretty much just throwing whatever you have in a pot and letting it simmer, there’s not too much to it.