GETTING TO the Milkweed Inn, run by chef Iliana Regan and her sommelier wife, Anna Hamlin, is not easy. The drive from Chicago to Michigan’s Upper Peninsula takes six hours, ultimately on rutted dirt roads deep inside the Hiawatha National Forest. And that’s if you’re able to get a room in the first place. The 2023 season and much of 2024’s are already sold out. There is some consolation, however, for fans who have followed Ms. Regan’s career from her Michelin-starred Chicago restaurant, Elizabeth, now closed, through her 2019 memoir, “Burn the Place,” an unflinching account of her farmhouse upbringing, her grappling with addiction and gender identity, and her emergence as a chef: Her new book, “Fieldwork” (Agate Midway), comes out Jan. 24.

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