In a saucepan, combine potatoes, carrots, onion, mushrooms, garlic, parsley, 1/4 cup butter, and milk. Bring to a boil on medium heat, then reduce to low and simmer until potatoes soften (add more milk if potatoes absorb all the liquid before they've softened or if milk doesn't cover potatoes). This should take about 10 minutes.
In a large soup pot, stir together evaporated milk, half & half, 1/4 cup butter, rosemary, and sherry. Add the cooked potato mixture and bring everything to a boil on medium-low heat, about 5 minutes.
Gently add shrimp to the pot and simmer 5 more minutes.