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To prepare the glaze: Stir together the cracked peppercorns, thyme leaves, olive oil, and garlic in a small bowl and season with salt.
To prepare the goose: Preheat the oven to 375 degrees F. Season the outside and the cavity of the goose with salt and pepper. Brush the glaze all over the outside of the goose, reserving any extra to use for basting. Place the onion, carrots, and celery in the raosting pan, and place the goose on top of the vegetables. Roast for 2 to 2 1/2 hours, basting occasionally with the remaining glaze and any drippings, until golden brown and crispy and the juice from the cavity runs clear. Remove the goose from the oven and let rest for 15 minutes before carving.
To prepare the sauce: Strain the pan drippings through a fine-mesh sieve, remove the fat, and place the juices in a small saucepan over medium heat. Whisk the butter into the meat juices, add the chopped thyme, and season to taste with salt and pepper.
Carve the goose and serve with the pan sauce.