Line two cookie sheets with parchment paper or silicone baking mats. Set aside until needed.
Place the butter and sugar in the bowl of a stand mixer fitted with the paddle attachment, and beat together on medium speed until light and fluffy. Scrape down the sides of the bowl, then add the cornstarch, vanilla, and rosemary, then mix again until well-incorporated.
In a medium bowl, whisk together the flour and salt, then add half the dry ingredients to the butter mixture. Mix on low speed until well-blended, scrape down the sides of the bowl, and add the remaining dry ingredients. Mix again on medium speed until a crumbly dough is formed: this may take a minute or so.
Use a small cookie scoop or two spoons to measure out tablespoon-sized balls of dough, then roll smoothly between your palms. Arrange on the prepared cookie sheets, flatten slightly, and use your thumb or the back of a measuring spoon to make little depressions in the center of each cookie. Transfer the trays to the refrigerator to chill for an hour, or to the freezer to chill for 15 minutes. This step ensures the cookies won’t spread out too much while baking.
When ready to bake the cookies, preheat the oven to 350°F. Remove the trays from the refrigerator or freezer and spoon orange marmalade into the depressions: for best results, keep the filling even with the top of the cookies and resist the urge to overfill.
Transfer the trays to the oven and bake for 18 to 20 minutes, rotating the trays halfway through. Remove from the oven and allow to cool for 5 minutes on the cookie sheets, then transfer to a cooling rack to cool completely. If desired, press a rosemary sprig into the marmalade filling on each cookie.
The cookies will keep in a covered container at room temperature for up to 5 days or can be frozen for up to 3 months.