Combine flour, almond flour, salt, and spices. In food processor, cream butter and add powdered sugar and Steen’s syrup. Mix until combined.
Add egg and rum. Mix, scraping down the bowl as needed to evenly combine all ingredients. Next add flour mixture and mix until combined. Cover and chill.
Toast pecans and add to food processor. Grind until no large chunks remain.
Add butter and mix. Add sugar and Steen’s syrup and mix until combined. Mix in eggs, rum, and vanilla and incorporate. Add flour and salt and mix just to combine. Cover and chill.
Rum Whipped Cream
Whip heavy cream to soft peaks and add powdered sugar. Whip until stiff peaks form.
Add rum and vanilla and mix to combine. Chill.
Once tart dough is chilled but pliable, press into 9½-inch greased tart pan. Chill until firm.
Spread frangipane halfway to top of tart pan and top with half the fruit and nut mixture. Fill the rest of the tart with remaining frangipane to just under top of tart pan. Arrange the remaining fruit and nuts in decorative pattern and gently press into the frangipane.
Chill until firm, about 10–15 minutes, while oven preheats to 325 degrees. Bake 25–30 minutes, rotating halfway through cooking. Tart is finished when frangipane is set and no longer liquid and when cake tester inserted in center comes out clean.
Remove from oven and let cool on rack before removing from tart pan. Spoon whipped cream onto tart. Serve slightly warm or at room temperature with a drizzle of Steen’s syrup.