Make the rosemary shortbread: Preheat the oven to 325°F (160°C). Line a 9 x 13-inch baking dish (preferably aluminum) with parchment paper.
Add the flour, sugar, rosemary, and salt to the bowl of a food processor and pulse a few times to incorporate. Add the butter and pulse until pebbly and the butter chunks are no larger than the size of peas, about 20 pulses.
Transfer the dough to the prepared baking dish and press down with your hands or a flat-bottomed measuring cup to compact into an even layer, ensuring the dough reaches all the corners and edges.
Bake for 25–30 minutes, until the edges are light golden brown. Remove from the oven and let cool completely (for faster cooling, let sit at room temperature for 15 minutes, then transfer to the refrigerator or freezer). The cooled shortbread can be wrapped in plastic wrap and kept in a cool, dry place for up to 2 days.
Make the sage caramel: Add the heavy cream and sage to a small saucepan. Bring to a simmer over medium heat. Let simmer lightly for a moment, then remove the pot from the heat and let the sage steep for at least 20 minutes. Strain, discarding the sage leaves, and set aside.
Add the sugar, corn syrup, and water to a medium, heavy-bottomed saucepan and gently swirl the pot to moisten the sugar completely. Attach a candy thermometer to the pot (or have an instant-read thermometer nearby) and bring to a boil over medium heat. Cook until the temperature reaches 320°F (160°C), 5–10 minutes. Remove the pot from the heat. Gradually pour in the sage-infused cream and whisk constantly to incorporate, being careful as the mixture will bubble and sputter. Whisk in the butter and salt to combine.
Return the pot to the heat and cook, whisking constantly for another 5–10 minutes, until the temperature reaches 240–245°F (115–118°C). Immediately remove the pot from the heat.
Pour the caramel over the cooled shortbread and use an offset spatula to smooth into an even layer. Transfer to the refrigerator to let the caramel set completely.
Once the caramel has set, prepare the decorations, then make the white chocolate ganache: Add the white chocolate, cream, and salt to a medium heatproof bowl. Microwave in 30-second intervals until beginning to melt, then stir or whisk until smooth.
Pour the ganache on top of the caramel and use an offset spatula to spread into a smooth, even layer. Immediately sprinkle the pomegranate arils, pistachios, and sprinkles, if using on top. Transfer to the refrigerator to set the chocolate.
Once firm, cut the shortbread into squares or diamonds. The cookies can be stored in an airtight container in the refrigerator for up to 5 days.