In an electric pressure cooker set on sear, melt 2 tablespoons butter over medium heat. Add onion and garlic, sauté until translucent, about 4 minutes. Add rice and cook, stirring, 1 minute more. Add wine and cook until wine evaporates, about 30 seconds. Add 3 cups of chicken stock; season with salt and pepper.
Secure lid. Set pressure cooker on rice setting for 10 minutes. Vent pressure, then remove lid. Reset to sear setting and stir in shrimp with remaining 1½ cups broth, and cook until shrimp are opaque, 3 to 5 minutes. Stir in cheese and remaining 2 tablespoons butter. Finish with herbs and serve immediately.