Stuffed Turkey Breast With Butternut Squash, Kale, and Sausage

Working one at a time, place turkey breast, skin side down, on a cutting board. Using a sharp knife and cutting parallel to board, slice through thickest part of breast, cutting along length of breast without cutting all the way through, then open breast like a book. Place breast in between 2 large pieces of plastic wrap and pound with a meat mallet to a uniform thickness of 1/2". Season inside of breast with 1 tsp. salt, 1/2 tsp. pepper, and 1/2 tsp. ground fennel. Transfer skin side up to a rimmed baking sheet; season with 1 tsp. salt, 1/2 tsp. pepper, and 1/2 tsp. ground fennel. Repeat with remaining breast. Let sit at room temperature 1 hour, or chill up to 24 hours for maximum flavor and juiciness (if chilled, let sit at room temperature 1 hour before roasting).
Arrange a rack in center of oven; preheat to 450°F. Heat oil in a large skillet over medium-high. Add sausage, stirring and breaking up into small pieces with a spoon, until browned and cooked through, 5–7 minutes. Using a slotted spoon, transfer sausage to a large bowl, leaving drippings behind.
Meanwhile, place croutons on a rimmed baking sheet. Crush slightly with the bottom of a small pot or pan until some pieces are smaller.
Return skillet to medium-high heat and melt 2 Tbsp. butter. Add onion, squash, chopped fennel, garlic, thyme, and remaining 1 1/2 tsp. salt and 1/2 tsp. pepper and cook, stirring occasionally, until softened, 6–8 minutes. Stir in kale, 2 Tbsp. butter, and 1 cup broth and cook, scraping up brown bits on bottom of pan, until kale is wilted and butter is melted, about 3 minutes. Transfer to bowl with sausage. Fold in croutons and parsley; if mixture seems dry, add 1/4 cup broth.
Flip breasts so they are skin side down. Divide stuffing between breasts, spreading with a spatula and leaving a 1" border. Starting at 1 short end, roll each breast into a log, completely enclosing stuffing, then transfer each to separate, large pieces of cheesecloth. Wrap cheesecloth around turkey and secure by tying a piece of twine at each end (like a sausage). Tie 4–5 pieces of twine crosswise around log, spacing about 2–2 1/2" apart. Rub remaining 4 Tbsp. butter all over breasts and transfer skin side up to roasting pan.
Pour enough broth (about 4 cups) to come 1/4" up sides of turkey. Reduce oven temperature to 375°F and roast turkey, basting with pan juices every 20 minutes and adding more broth if pan starts to dry out, until an instant-read thermometer inserted into the center reads 155°F, 60–70 minutes.
Transfer to a cutting board and let sit 15–20 minutes (internal temperature should rise to 165°F). Remove twine and slice crosswise about 1/2" thick to serve.
Turkey can be seasoned 2 days ahead and stuffed, rolled in cheesecloth, and buttered 1 day ahead; loosely cover and chill. Let sit at room temperature 1 hour before roasting.