Toss beef with epis, lime juice, 1 teaspoon salt, and pepper. Marinate for 30 minutes. Heat oil in a Dutch oven and brown beef in batches.
Return beef to the pot with 2 cups stock. Cover and simmer for 45 minutes until partly tender.
Cook the Vegetables:
Add eggplant, cabbage, chayote, carrots, spinach, onion, garlic, tomato paste, thyme, Scotch bonnet, remaining salt, and remaining stock. Cover and cook for 35 to 40 minutes until very soft.
Mash and Finish:
Remove the whole pepper and thyme stems. Lift the beef out briefly, then mash the vegetables into a thick cohesive mixture, leaving some natural texture.
Return the beef and simmer uncovered for 10 minutes, stirring often, until the legim is thick enough to mound on a spoon.
Notes
Keep the Scotch bonnet whole for aroma with restrained heat; discard it before mashing.
Legim improves overnight and keeps refrigerated for four days.