Prepare dough in bread machine: Add milk, eggs, sugar, salt, bread flour, softened butter, and instant yeast into the bread machine pan. Use the dough function on your bread machine to mix and proof the dough. Peek inside occasionally to check progress.
Make caramel syrup: While dough proofs, melt butter in a pan, add granulated sugar, honey, vanilla extract, and fine sea salt. Cook over heat until sugar dissolves to form a caramel syrup.
Divide and shape dough: Turn the risen dough out onto a work surface. Cut into three portions, then cut each portion into five smaller pieces.
Coat dough pieces: Melt butter and mix with sugar and ground cardamom. Coat each dough piece in melted butter, then roll in the sugar-cardamom mixture.
Assemble and proof: Pile the coated dough pieces into a baking pan. Cover with a clean towel and let proof for 30 to 45 minutes, or up to an hour depending on kitchen temperature.
Bake monkey bread: Pour the cooled honey vanilla caramel syrup over the dough pieces in the pan. Bake in a preheated oven at 350°F (175°C) for 40 to 50 minutes until golden and cooked through.
Serve: Serve the monkey bread straight from the pan or invert it onto a plate for a dramatic presentation.