Do not remove the flan from the refrigerator until ready to serve. Unmold just before serving.
Preheat oven to 325 degrees. Bring 1 cup maple syrup to a boil in a medium saucepan over medium heat. Boil, stirring occasionally, until reduced to 2/3 cup, about 10 minutes. Remove from heat and let cool just until foam subsides. Pour into an 8-inch round cake pan, tilting pan to evenly coat bottom and sides to rim. Place cake pan in center of a roasting pan.
Gently whisk together eggs, egg yolks, half-and-half, salt, and remaining 3/4 cup syrup in a bowl. Skim off and discard any foam from surface. Pour mixture through a fine-mesh sieve into cake pan. Pour enough scalding-hot water into roasting pan to come halfway up sides of cake pan.
Bake until flan is set along edges but still very wobbly in center, 50 to 60 minutes. (Flan will continue to set as it cools.) Carefully remove pan from hot-water bath and place on a wire rack; let cool completely. Cover and refrigerate until cold, at least 4 hours.
When ready to serve, run a thin-bladed knife between flan and sides of pan to loosen. Place a rimmed plate or platter upside down over pan, then hold onto pan and plate and quickly invert together. Carefully lift pan, tapping on bottom if necessary to release flan. Cut into wedges and serve immediately.