01 - Heat olive oil and butter in a large deep skillet or Dutch oven over medium heat until butter melts and begins to foam.
02 - Add onions, carrots, and celery to the pan. Sauté for 5-6 minutes, stirring occasionally, until vegetables soften and onions become translucent.
03 - Stir in minced garlic and cook for 30 seconds until fragrant, being careful not to burn it.
04 - Sprinkle flour evenly over the vegetables, stirring constantly to coat. Cook for 1-2 minutes to remove raw flour taste and create a light roux base.
05 - Gradually whisk in chicken broth and milk or half-and-half, stirring continuously to prevent lumps from forming.
06 - Add dried thyme, sage, salt, and black pepper. Bring mixture to a gentle simmer and cook for approximately 5 minutes until sauce thickens enough to coat the back of a spoon.
07 - Add uncooked gnocchi, shredded chicken, and frozen peas to the pot. Stir gently to combine, ensuring gnocchi are fully submerged in the liquid.
08 - Cover the pot and reduce heat to maintain a gentle simmer. Cook for 10-12 minutes, stirring occasionally to prevent sticking, until gnocchi float and feel tender when tested.
09 - Remove from heat and stir in grated Parmesan cheese until melted and incorporated, if using.
10 - Sprinkle with freshly chopped parsley before serving hot.