Heat oil in a large saucepan over medium heat. Stir in garlic and cook until lightly browned, about 5 minutes. Pour in 1 cup of chicken stock, cover, and allow to simmer until the garlic is soft, about 10 minutes.
Mash the garlic with a fork into a coarse paste. Pour in remaining chicken stock, increase heat to medium-high, and bring to a boil. Stir in carrots and cook for 1 minute, then add red pepper and continue cooking until vegetables are tender. Season to taste with salt and pepper before serving.