1. In a large bowl, using a hand mixer beat together butter and sugar until fluffy, about 2-3 minutes. Add egg and beat for 1 minute. Add maple syrup and beat to combine, about 1 minute.
2. In a medium sized bowl, combine flour and salt. Add flour mixture to butter mixture and mix until dough comes together, about 1 minute.
3. Dump dough onto a lightly floured surface. Shape into two round discs, wrap in plastic wrap and place in fridge for 1 hour.
4. Preheat oven to 350°F. Line two baking sheets with parchment paper.
5. On a lightly floured surface, roll out one disc of dough until ¼” thick. Use extra flour if dough is sticky. Cut out 2” rounds, and place 1” apart on prepared baking sheets.
6. Bake cookies for 8-10 minutes, until dough is just starting to turn golden brown around the edges. Let cool and repeat with remaining dough.
7. Make icing by combining butter and icing sugar with a hand mixer. Mix on medium speed until combined, about 2 minutes. Add maple extract and cream, and continue to mix on high speed until icing is light and fluffy, about 5 minutes.
8. Pipe icing using a star tip or spoon, about 1 Tbsp icing on the inside of one cookie. Sandwich cookies together and repeat with remaining cookies.