Pour tomatoes and juice into a nonreactive bowl; hand crush, discarding any hard cores and skin and set aside.

Trim and discard any fat from beef; lay on a flat work surface. Combine salt, pepper, and cayenne; sprinkle half of mixture evenly over meat. Using a meat mallet or small heavy skillet, pound meat until thin; turn, sprinkle with remaining salt and pepper mixture and pound to an even ¼-inch thickness. Cut into pieces about 2 to 3 inches square.

Place a large Dutch oven over medium-high heat; add lard or cooking oil and heat until oil shimmers. 

Place flour in a pie pan; working in batches, dredge seasoned meat in flour and fry, turning once, until browned on both sides. Remove to a plate and repeat until all meat is browned. Reduce heat to medium, deglaze pan with a little water or red wine if necessary; add onion, celery, and green pepper and sauté until vegetables soften, about 10 minutes. Add garlic and cook until fragrant, about 30 seconds. Add crushed tomatoes and juice, water or broth, and bay leaf; stir to combine and bring to a high simmer. Add browned meat to pot, reduce heat to medium-low and cook, stirring from time to time and adding additional liquid if necessary, until gravy has thickened and meat is tender, about 1½ hours. Serve over Cheese Grits, garnish with sliced green onions. 

Cheese Grits

Place water and milk in a large heavy saucepan over medium-high heat; bring to a boil. Slowly whisk in grits, return to a boil, reduce heat to medium-low and simmer, stirring from time to time until thickened, about 10 minutes. Add cheeses and butter and stir until melted; taste and adjust seasoning. Note that salt content in cheeses will vary; salt accordingly. Serve at once.

Note: Substitute stone-ground grits; add an extra cup of liquid, and increase cooking time to almost 1 hour.