Thai coconut and red curry soup

I'm trying to recreate a Thai hot pot from Noodles.  This is pretty darned close and I'm happy with being able to make it at home.

The base of the soup comes from Budget Bytes.

2 tbs neutral oil
1 chopped carrot
2 cloves of garlic, minced
1 tbs grated fresh ginger
3 tbs red curry paste
4 c. chicken broth
13 oz can coconut milk (not light)
1/2 tbs fish sauce
1/2 tbs brown sugar
3.5 oz cooked rice noodles
Snow peas cut on the diagonal
cilantro leaves, chopped
green onions, sliced
lime segments

Cook the carrot in oil until fragrant and starting to soften.
Add the garlic, ginger, and curry paste and cook 1 minute.
Add the chicken broth and bring to a simmer.
Add the coconut milk, fish sauce and brown sugar.
To serve, place noodles in the bottom of the bowl then top with soup.
Add cilantro, snow peas and green onions to taste.
Serve with fresh lime juice.