In an ovenproof skillet, add sugar and 1/2 cup water, and heat gently on the stovetop to melt sugar. Once the sugar has melted, increase the heat so the mixture is bubbling for about 5 minutes and a light caramel forms. Remove the skillet from the heat and stir in the butter. Add the apricots, arranging them cut-side down, packed tightly in the caramel. Set aside to cool.
On a floured surface, roll out the pastry dough and trim to a circle that is about one inch larger than the skillet. Lay the pastry over the apricots in the pan and tuck the edges in. Bake for 30 to 35 minutes until puffed and golden.
Prepare the cream:
In a medium chilled bowl, whisk the cream and mascarpone until peaks begin to form. Add honey and vanilla and continue to whisk until peaks are medium. Chill until ready to use.
Remove the tart from the oven and let sit for 5 minutes. Cover it with a large serving plate and flip the pan, removing it. Scatter with pistachios and dollop with mascarpone cream.