In a saucepan, bring the broth and milk to a simmer
In a big soup pot, heat the butter over medium-high heat until foamy.
Add the garlic and cook, stirring, until fragrant (~ 1 minute)
Reduce the heat to medium, add the flour, and cook, stirring, until toasty and foaming (~ 2 to 3 minutes)
Whisk in the broth-milk mixture, slowly at first, then add the salt and pepper. Bring to a boil, then reduce the heat and cook until thickened (~ 5 minutes)
Add the potato, carrots, peas, pearl onions, and ham and simmer until the potatoes are tender (~ 20 minutes)
Stir in the chicken and cream and heat through for 5 additional minutes.
Season with salt and pepper to taste and serve with the broken pie crust on the side.