Cut the squash in half lengthwise. With a large spoon, scoop the seeds from the center of the squash and discard.

Place the squash halves cut side down in a large skillet. Roast for about 40 minutes, then place on a plate to cool.

When the squash is cool enough to handle, cut into large dice. (if you use acorn squash, do not remove the skin, if you use butternut squash, you will likely prefer it without the skin.)

Place 2 teaspoons of the olive oil in a large skillet over medium-high heat. Add the onions and saute for about 4 minutes, then add the mushrooms and continue cooking for another 4-5 minutes.

Add the sausage and continue sautéing for another 4 minutes.

Add the salt, sage, honey, vinegar, and pepper, stir thoroughly, and remove from heat. Cool on the counter for a few minutes, then add the diced squash, stir gently, and place in the refrigerator while prepping the turkey breast for stuffing.

Place a large skillet in the oven and bring the temperature to 375F.

When ready to stuff, place the turkey breast skin side down on a cutting board so that the two halves of the breast are in a butterfly pattern (vertical to you). Cover the breast with plastic wrap. Using the bottom of a small, heavy saucepan or the flat side of a meat mallet, pound the breast gently until it is uniformly about 1/2 inch thick.

Spread the cooled vegetable mixture evenly over the flattened turkey breast and pat down until uniformly thick. Fold each outer edge toward the center so that they slightly overlap to form a tube. Using cotton twine, truss the breast.
Place the remaining 1 teaspoon of olive oil in the preheated pan and place the trussed breast in the pan seam side down (skin side up).

Roast for 15 minutes at 375F, then reduce the heat to 325F and roast for an additional 35 minutes. Throughout the time the breast is cooking, baste the skin with the drippings from the pan about every 10 minutes.

Slice and serve.