Cut the cabbage in half through the core, then slice each half into 3 or 4 wedges, ensuring each piece retains a portion of the core to hold its shape during cooking.

Heat 15 ml of olive oil and 15 ml of butter in a wide, deep skillet or Dutch oven over medium-high heat. Season the cabbage wedges with salt and pepper.

Place cabbage wedges cut-side down in the hot skillet. Sear undisturbed for 3 to 4 minutes per side until deeply browned and caramelized, working in batches if needed. Transfer seared wedges to a plate.

Reduce the heat to medium. Add the remaining butter to the skillet, then sauté the minced garlic, chopped sun-dried tomatoes, oregano, and red pepper flakes for about 1 minute until fragrant.

Pour in the vegetable broth and heavy cream, stirring and scraping up any browned bits stuck to the bottom of the skillet. Bring the liquid to a gentle simmer.

Nestle the seared cabbage wedges back into the sauce. Cover the skillet tightly with a lid, reduce heat to low, and braise for 20 to 25 minutes until the cabbage is buttery and fork-tender.

Remove the lid and sprinkle the grated Parmesan cheese evenly into the bubbling sauce. Simmer uncovered for 2 to 3 minutes until the sauce slightly thickens, spooning the pan juices over the cabbage wedges.

Remove from heat, garnish generously with fresh basil, and serve immediately alongside crusty bread or over polenta.