Dice all vegetables and chicken into similarly sized pieces (approximately ½-inch cubes) to ensure even cooking. If using bacon, place it in the freezer for 10 minutes before chopping for cleaner cuts.
Heat olive oil in a large Dutch oven over medium heat. If using bacon, add it and cook until crisp (5-6 minutes). Remove bacon with a slotted spoon and set aside, leaving the fat in the pot.
Add onions, carrots, and celery to the pot and sauté until vegetables begin to soften, about 5 minutes. Add garlic and cook for 30 seconds until fragrant.
Add chicken pieces to the pot and season with salt, pepper, thyme, rosemary, and nutmeg. Cook until chicken is nearly opaque on all sides, about 4-5 minutes.
Sprinkle flour over the mixture and stir continuously for 2 minutes to cook out the raw flour taste.
Gradually pour in chicken broth while stirring constantly to prevent lumps. Add diced potatoes, bring to a simmer, and cook until potatoes are just fork-tender, about 10-12 minutes.
Reduce heat to low and stir in heavy cream and frozen peas. Simmer gently for 3-4 minutes until soup is heated through and slightly thickened. Return the reserved bacon to the pot and adjust seasonings to taste.
Serve hot with your choice of toppings, such as buttery biscuits, puff pastry squares, homemade croutons, or crispy potato gnocchi.