Preheat the oven to 400F. In a deep saute pan, melt 1 tablespoon of the butter. Add the carrot, leek, and thyme and saute just until tender, about 4 minutes. Season with salt and pepper, and transfer to a bowl. Add the shredded turkey to the vegetables and set aside.
In the same pan, melt the remaining 3 Tablespoons butter. Add the flour and cook, stirring, until the mixture starts to brown. Slowly add the broth, whisking constantly, then the milk.
Whisk until smooth and let simmer until the sauce thickens, about 2 minutes. Whisk in the wine, and season to taste with salt and pepper.
Pour the sauce into the bowl with the turkey and vegetables. Add the peas, and stir to combine. Season to taste with salt and pepper. Divide the mixture between four or five 1-cup ramekins.
Top with dollops of mashed potatoes and bake until the potatoes are golden on top and mixture is bubbling, about 25 minutes.