Allow frangipane to come to room temperature, if it was stored in the fridge. Pre-heat oven to 350F, with a rack in the middle position. Line a sheet pan with parchment if you haven't already with blind-baking the pate brisee shell.
Slice 2-3 small to medium apples into thin (about 1/4") slices. Keep sections of the slices together if you want to fan them out in the frangipane.
Spread frangipane into the blind-baked tart shell into an even layer. Arrange the apple slices in the frangipane, gently pressing them in.
Bake tart for 30-40 minutes, until the frangipane is golden and puffed.
Once out of the oven, gently heat 3 TB maple syrup in a small pan, allowing it to bubble for 30 seconds to reduce. Brush evenly over the still warm apples, re-heating the reduce maple syrup if it gets too cold and sticky while glazing. Grate nutmeg and cinnamon over the maple glazed apples, if desired.
Allow tart to cool before cutting. Store covered at room temp up to 2 days, or a few days in the fridge.