Place potatoes into a large pot and cover with water; stir in the 1/2 teaspoon salt. Bring to a boil over high heat, then reduce heat to medium-low, cover, and simmer until tender, about 20 minutes.
Drain.
Place drained potatoes, butter, the 1/3 cup milk, the 1/2 teaspoon salt, and pepper in a large bowl.
Mix well with an electric mixer on medium speed until smooth. Cover and set aside until ready to use.
Preheat oven to 375 degrees F. Cook ground beef over medium heat in extra-large skillet for 8 to 10 minutes or until browned, stirring frequently.
Drain off fat.
Add onions and carrots to skillet. Cook, stirring occasionally, for 5 minutes or until carrots are just tender.
Add cream cheese, the remaining 1/3 cup milk, Worcestershire sauce, and basil. Reduce heat to low. Cover and cook for 5 minutes or until cubes of cheese are soft. Stir to combine. Stir in peas.
[Cleaning tip: Once the stove top is cool, wipe up any oil splatters or spills with Clorox® Disinfecting Wipes*.]
Spoon the beef mixture into a 2-quart casserole dish. Top with the mashed potato mixture.