Pat ribs dry with paper towels. Season all over with kosher salt and freshly ground black pepper. Lightly dust the ribs with the all-purpose flour, shaking off excess. Heat a large ovenproof Dutch oven or heavy pot over medium-high heat. Add vegetable oil and butter until shimmering. Sear the ribs in batches (do not crowd) 3–4 minutes per side until deeply browned. Transfer browned ribs to a plate.

Sweat aromatics

Reduce heat to medium. Add the chopped onion, carrot, and celery to the pot; cook, stirring occasionally, until softened and starting to brown, about 6–8 minutes. Add minced garlic and cook 30–45 seconds until fragrant. Stir in tomato paste and cook 1–2 minutes to caramelize the paste, stirring so it doesn’t burn.

Deglaze and braise

Pour in the dry red wine to deglaze, scraping up browned bits from the bottom with a wooden spoon. Let the wine reduce by about half, 3–4 minutes. Add beef or game stock, Worcestershire sauce, thyme sprigs, and bay leaf. Return the short ribs and any accumulated juices to the pot so they are partially submerged (liquid should come about halfway up the ribs). Bring to a gentle simmer on the stovetop.

Oven braise

Cover the pot with a lid and transfer to a preheated 325°F (160°C) oven. Braise until very tender and falling from the bone, about 2 to 2½ hours depending on thickness. Check once halfway through to ensure liquid level and baste the ribs with the braising liquid if needed.

Finish sauce

When ribs are tender, transfer ribs to a warm plate and tent with foil. Place the pot on the stovetop over medium-high heat and reduce the braising liquid until slightly thickened, about 6–8 minutes. Remove and discard thyme stems and bay leaf. Skim any excess fat from the surface. Taste and adjust seasoning with salt and pepper.

For the creamy corn polenta

Bring water and milk to a simmer in a medium saucepan over medium heat. Add salt. Slowly whisk in the cornmeal in a steady stream to avoid lumps. Reduce heat to low and simmer, stirring frequently with a wooden spoon, until thickened and the grains are tender, about 20–25 minutes (follow package directions for cook time if different).

Stir in the butter, grated Parmesan, and fresh corn kernels. Continue cooking 1–2 minutes to warm the corn. Adjust seasoning with salt and freshly ground black pepper. If polenta becomes too thick, whisk in up to 2 tablespoons hot water or milk to loosen to a creamy consistency.

Cover and keep warm off heat until ready to plate, stirring occasionally to prevent a skin from forming.

For the summer herb gremolata & finish

Combine the finely chopped parsley, chopped mint, lemon zest, minced garlic, extra-virgin olive oil, sea salt, and freshly ground black pepper in a small bowl. Stir to combine. Taste and adjust lemon zest, salt or mint to your preference. Stir in shaved Parmesan if using.

To serve: Spoon a generous portion of creamy corn polenta onto each plate. Place an elk short rib on top or beside the polenta. Spoon some of the reduced braising sauce over the ribs and a little onto the polenta. Sprinkle the summer herb gremolata over the ribs and polenta to add bright, fresh contrast. Garnish with an extra thyme sprig or lemon wedge if desired.