Melt butter in a large pot over medium-high heat. Add leek, carrots and celery; cook, stirring occasionally, until softened and translucent, 6 to 8 minutes. Reduce heat to medium, add garlic and flour and cook, stirring constantly, until the garlic is fragrant and the flour has toasted, about 1 minute. Slowly add broth, stirring constantly. Add milk, pepper and salt and bring to a simmer (do not boil) over medium-high heat, stirring often and scraping the bottom of the pot to release any browned bits.