Preheat the oven to 400 degrees Fahrenheit.
Add the butter to a large 12inch oven safe skillet over medium heat.
Add in the onions, and cook them in the butter for about 5 minutes.
Add the carrots and celery and sauté them in the butter for another 3 to 5 minutes, stirring occasionally, until they are slightly tender.
Add in the flour and stir it to coat the vegetables in it, and cook for another 1 to 2 minutes.
Slowly pour in the chicken broth and heavy cream, whisking the flour mixture into them to get rid of any lumps.
Continue to let the mixture simmer for about 5 to 10 minutes, or until the sauce has thickened.
Stir in the chicken, frozen peas, and seasonings, and stir to heat everything up.
Arrange the biscuits evenly on top of the chicken filling.
Brush the tops of the biscuits with melted butter.
Bake for about 15 to 20 minutes, or until the biscuits are golden and cooked through and the pie filling is hot and bubbly.
Let rest for 10 minutes, then serve warm.