Place the potatoes and carrots in a medium saucepan and cover with cold water. Bring to a boil over moderate heat, and cook until just fork tender, about 12 to 15 minutes. Drain, transfer to a large bowl and set aside.

Set a large skillet over medium-high heat with 1 tablespoon butter. Once melted, add in the chicken and cook, stirring often, until just starting to brown and almost cooked through, about 3 to 4 minutes. Carefully drain any liquid, if any, that has accumulated in the pan. Add the remaining tablespoon of butter to the skillet and then stir the onion, garlic, and celery. Cook until the veggies have softened and the chicken has fully cooked through, about 5 minutes. Season with salt, pepper, and thyme. Deglaze the pan with the white wine and cook until it's almost all evaporated, about 5 minutes. Remove from the heat, stir in the peas and transfer everything to the large bowl with the potatoes and carrots and set aside to cool completely.

Once cooled, stir in the mayo and parsley. Give it a taste and adjust seasonings as needed, adding more salt or pepper if necessary. Cover with plastic wrap and chill for at least 1 hour. To assemble the sandwiches, split open the biscuits and fill each with a heaping amount of the chilled salad. Place the top part of the biscuits on top and serve immediately. Enjoy!

To make the biscuits: preheat oven to 425°F. Line a baking sheet with parchment paper and set aside.

In a large bowl, whisk together the flour, baking powder, baking soda, salt and sugar. Add the cold butter and working quickly, use your finger tips to rub the butter into the dry ingredients until it resembles coarse crumbs of varying sizes. Make a well in the center of the bowl and add in the buttermilk. Using a rubber spatula, stir until the mixture just comes together. Dump out onto a floured work surface and knead until the mixture forms a rough looking dough. Roll out into a rectangle and then fold over onto it self. Rotate and roll out once more, folding again and repeating the process once more. Finally, roll out to a rectangle that is 1-inch thick. Cut out into eight rounds using a 4-inch biscuit cutter. You might have to rework the scraps to get all eight. Place the biscuits onto the prepared baking sheet, placing them close to each other without touching. Freeze for 10 minutes. Brush the tops with melted butter, reduce the oven temperature to 400°F and bake until golden brown, 20 to 25 minutes. Biscuits can be made up to 2 days in advance and stored in the fridge. Just rewarm before assembling.