Mix the syrup and cider together in a bowl and add the squirrel pieces. Marinate overnight.
The next day, mix the flour, salt and pepper together and roll in the flour; set aside for now.
Meanwhile, pour chicken broth in Dutch oven with the butter, mushrooms and onion.
Preheat oven to 275 degrees.
Heat the butter in a skillet and brown the squirrel meat on all sides; add to the Dutch oven. Bake for 90 minutes, covered, and if it is not fork-tender, bake for another 30 to 45 minutes.
For gravy, just remove the mushrooms and add a slurry of water and flour. Whisk until thickened and put the mushrooms back in. Serve the gravy over the squirrel with mashed potatoes and roasted asparagus.