Pat the shrimp dry and sprinkle with dried basil, then season lightly with salt and freshly ground black pepper; toss to coat.
Heat 1 tablespoon butter in a 12-inch nonstick skillet over medium-high heat until melted and hot.
Add shrimp in a single layer and cook until the bottom side is pink, then flip and cook the other side until shrimp are cooked through and pink, about 3 minutes total; transfer shrimp to a plate.
Reduce heat to medium and melt the remaining 1 tablespoon butter in the same skillet.
Add minced garlic and sauté until just fragrant and lightly golden, about 30 seconds.
Pour in 3/4 cup chicken broth, add the chopped spinach, and cook while stirring until the spinach starts to wilt, about 1 minute.
Whisk the cornstarch mixed with 1 tablespoon chicken broth into the heavy cream, then pour the cream mixture into the skillet and cook, stirring constantly, until it begins to simmer and thicken slightly, about 2 minutes.
Stir in the shredded Parmesan until melted and smooth; taste and season lightly with additional salt if needed.
Remove the skillet from heat, return the cooked shrimp to the sauce, and toss to coat; serve immediately over spaghetti or spaghetti squash if desired.
