Melt 2 tablespoons of the butter in a saucepan over medium heat. Add the chopped onion and cook until tender, about 5 to 7 minutes.
Stir in the peas and the chicken stock and cook for about 4 to 6 minutes stirring occasionally, until the peas are warmed through and bright green.
Add the nutmeg and dry mustard to the cooked peas and onions. Remove from heat and set aside while you make the sauce.
In a large saucepan, melt the remaining 4-½ tablespoons of butter over medium heat. Whisk the flour into the butter until smooth.
Add the kosher salt and the black pepper, whisking into the butter and flour. Cook for about 3 minutes.
Add the kosher salt and the black pepper, whisking into the butter and flour. Cook for about 3 minutes.
Whisk the milk into the butter and flour. Continue cooking over medium heat until the mixture thickens slightly about 20 minutes, stirring occasionally with a whisk.
Pour the sauce into the peas. Using an immersion blender, purée until smooth.
Return the pan to a medium heat, pour the half and half into the soup and heat until warmed through.
Garnish with a touch of sour cream if desired.