Heat the olive oil in a large saucepan over medium heat. Add the minced rosemary and stir for 30 seconds before adding the onion and carrots.
Once the onion is translucent, add the garlic, salt, and pepper. Cook and stir until the garlic is fragrant.
Add the butter. Once melted, stir in the flour. Continue stirring until the flour turns golden brown and the mixture has thickened.
Slowly pour in the evaporated milk and stir to combine. Once thickened, pour in the chicken broth. Add the shredded chicken, chicken bouillon, black pepper, paprika, and rosemary stalks. Cover and simmer for 10 minutes.
Remove the rosemary stalks and add the quartered biscuits. Cover and simmer for 10 minutes, or until the biscuits are fully cooked.