In the bowl of a stand mixer fitted with the paddle attachment, beat 1⅓ cups (167 grams) flour, sugar, yeast, salt, poultry seasoning, and thyme at medium-low speed until well combined.

In a medium saucepan, heat milk, ⅔ cup (160 grams) water, and ¼ cup (56.5 grams) butter over medium heat until butter is melted and an instant-read thermometer registers 120°F (49°C) to 130°F (54°C). Add warm milk mixture to flour mixture, and beat at low speed until combined, stopping to scrape sides of bowl. Add 1 egg (50 grams), and beat until combined, stopping to scrape sides of bowl. Gradually add 2⅔ cups (333 grams) flour, beating just until combined and stopping to scrape sides of bowl.

Switch to the dough hook attachment. Beat at low speed until a soft, somewhat sticky dough forms, 7 to 9 minutes, stopping to scrape sides of bowl and dough hook; add up to remaining ¼ cup (31 grams) flour, 1 tablespoon (8 grams) at a time, if dough is too sticky. (Dough should pass the windowpane test [see Note] but may still stick slightly to sides of bowl.) Turn out dough onto a very lightly floured surface, and gently shape into a ball.

Spray a large bowl with cooking spray. Place dough in bowl, turning to grease top. Cover and let rise in a warm, draft-free place (75°F/24°C) until doubled in size, 35 to 50 minutes.

Punch down dough; cover and let stand for 5 minutes.

Punch down dough. Turn out onto a lightly floured surface, and divide into 30 portions (about 35 grams each). Roll each portion into a ball, pinching any seams closed if needed.

Line a baking sheet with parchment paper. Place lid of Brie container or a 4½-inch round cutter in center of prepared pan. Place 12 dough balls in a circle around lid or cutter, leaving a ¼-inch gap between dough balls and between balls and lid. Place remaining dough balls, evenly spaced and almost touching, ¼ inch outside first circle. Cover and let rise in a warm, draft free place (75°F/24°C) until dough holds an indentation when poked, 35 to 45 minutes.

Preheat oven to 350°F (180°C).

In a small bowl, whisk remaining 1 egg (50 grams), and brush onto dough. Remove lid or cutter, and place Brie in center of rolls.

Bake until golden brown, 20 to 25 minutes.

Meanwhile, in a small saucepan, cook sage, chopped rosemary, and remaining ¼ cup (56.5 grams) butter over medium heat, stirring occasionally, until butter is melted. Immediately brush hot rolls with butter mixture. Garnish with Hydrated Cranberries and rosemary sprigs, if desired.