In a medium skillet set over medium heat, melt together the 2 tablespoons butter and 3 tablespoons sugar, stirring occasionally, until the sugar just begins to caramelize, 3 - 5 minutes. Reduce the heat to medium-low, add the pine nuts and stir constantly until the nuts are toasted and coated in caramel goo, about 2 minutes (watch closely, as pine nuts are delicate and burn easily). Turn out onto a plate or sheet of parchment, spread into a single layer, and set aside to cool. Break up into clumps of 1 - 3 nuts.
In the same skillet, melt the stick of butter with the minced rosemary and set aside to steep and cool slightly. In the bowl of a stand mixer fitted with the paddle attachment, whip the eggs with 3/4 cup of sugar on medium-high until thickly foamy and lightened in color, about 5 minutes. Sift together the flour, salt and baking powder into a medium bowl. With the mixer on low, add the infused butter, stirring until combined, then the flour mixture, and finally the caramelized pine nuts. Remove the bowl and give the dough a final fold with a rubber spatula, making sure it is homogenous. Chill the dough until firm enough to handle, about 1 hour.
Position two racks in the upper and lower thirds of the oven and preheat to 350º. Line 2 baking sheets with parchment paper.
Divide the dough in half. Shape each piece into a log 14" long, 1" high and 2" wide. Place longways on the baking sheet spaced at least 3 - 4" apart. (you can use one sheet for both, but you will need both sheets for the cut cookies.)
Bake the logs until golden, firm, and cooked through, about 25 minutes, rotating once or twice. Let the logs cool on the sheets for at least 15 minutes. (At this point, you can wrap and freeze the logs to be baked later if you like.) Use a wide metal spatula to remove a log to a cutting board. With a large serrated knife, cut the log on a shallow diagonal into 1/2 - 3/4" slices. (I like to saw once toward myself, then press straight down to minimize crumbling, but do whatever works for you.) Place the cookies on the lined sheets and repeat with the other log.
Bake the cookies a second time until dried and golden, about 15 minutes, flipping the cookies over halfway through if they are browning more on the underside. Let cool.
These biscotti keep well, in an airtight container, for at least 2 weeks. The rosemary flavor will become more pronounced as they sit. Serve with an espresso, or perhaps a bowl of olive oil ice cream for an unusual dessert.
Nutritional values are based on one of three biscotti.