How to Make It
In a medium bowl, mash half of the strawberries with a potato masher. In a medium saucepan, whisk the mashed and chopped strawberries with the lemon zest and juice, the vinegar, salt, pepper and 1/3 cup of water. Sprinkle the pectin evenly on top, then whisk until incorporated. Bring the mixture to a rolling boil over high heat. Whisk in the sugar, return to a boil and cook over high heat until the sugar dissolves, about 1 minute. Remove from the heat and skim off any foam. Let the jam cool. Scrape into a bowl, cover with plastic wrap and refrigerate for at least 4 hours or overnight.
In a large bowl, whisk the flour with the salt, pepper, baking powder and baking soda until evenly combined. In the bowl of a stand mixer fitted with the paddle, beat the butter and sugar at medium speed until light and fluffy, about 3 minutes. Beat in the eggs one at a time until incorporated. Add the dry ingredients and beat at low speed until just combined. Make ahead: The dough can be stored in the refrigerator for up to 3 days.
Preheat the oven to 375°. Using a 1 1/2-ounce ice cream scoop or a soup spoon and working in 2 batches, scoop the dough into 11/2-inch balls and arrange at least 3 inches apart on 2 parchment paper–lined baking sheets. Bake the cookies for 12 to 14 minutes, until set at the edges and lightly browned; rotate the baking sheets from top to bottom and front to back halfway through baking. Let the cookies cool for 10 minutes, then transfer to a rack to cool completely.
To serve, spread 1 heaping tablespoon of the strawberry jam on one side of half the cookies. Sandwich with the remaining cookies and serve.