Preheat the oven to 375˚F. Debone the turkey legs, removing the entire thigh bone and two-thirds of the drumstick bone, leaving the end piece of the drumstick for presentation and ease of eating. Remove all of the tendons.
In a large saute pan on high heat, add the olive oil and butter. Add shallots and garlic, and cook to just soften without letting them color. Add mushrooms and cook, stirring occasionally, until their liquid has released and evaporated and the mushrooms are slightly browned. Deglaze the mushrooms with the white wine, if using, or broth. After the wine has evaporated, season the mushrooms with salt and pepper, and finish with the thyme. Remove from the heat and cool.
Once cool, finely chop the mushroom mixture. Season the deboned leg with salt and pepper. Using a pastry brush, brush the inside of the turkey leg with Dijon mustard. Spoon the mushroom mixture in the middle of the deboned turkey leg. Starting with the end that is closest to you, roll the turkey leg around the mushroom mixture, forming a roulade. Using kitchen twine, tie the leg tightly to ensure the roulade holds its shape.
Season the turkey roulades with salt and pepper. Roast until golden brown and the internal temperature reaches 165˚F, about 45 minutes. Let rest 10 to 15 minutes. When ready to serve, remove kitchen twine and slice with an electric knife.
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