Set a large, deep skillet over medium heat. Add the olive oil and unsalted butter, letting the butter melt until foaming.

Stir in the minced garlic, sliced sun-dried tomatoes, dried oregano, and red pepper flakes. Sauté gently until fragrant, taking care not to brown the garlic.

Pour in the vegetable broth and heavy cream, stirring continuously to lift any browned bits from the bottom of the pan. Bring the mixture to a gentle simmer.

Add the uncooked potato gnocchi directly into the simmering sauce. Stir to coat and cook uncovered, stirring occasionally, until the gnocchi are tender and plump.

Fold in the grated Parmesan cheese and baby spinach. Continue simmering until the cheese melts into a smooth sauce and the spinach wilts completely.

Season with kosher salt and black pepper to taste. Remove the skillet from the heat, scatter the fresh basil across the top, and serve immediately.