Preheat the oven to 350 F / 175 C and line two large baking sheets with silicone baking mats or parchment paper. Set aside.
In a large bowl or the bowl of a stand mixer, beat 1 cup butter and 1 cup granulated sugar and mix on a medium-high speed for a couple of minutes, until the mixture becomes lighter in color.
Then mix in 3 Tbsp of strawberry reduction, 1 large egg + 1 large egg yolk, 1 tsp vanilla extract, and a small drop of red gel food coloring (optional) on a medium speed until fully incorporated. Scrape the sides and bottom of the bowl as needed with a rubber spatula.
Add 2 1/2 cups flour (use a scale or fluff the flour in the bag, then spoon it into the measuring cup and level it), 2 tsp baking powder, and 1 tsp fine salt, and mix on low speed until it is JUST incorporated. Scrape the sides of the bowl with a rubber spatula.
There are two options for using the rest of the strawberry reduction - you can either marble some of it into the cookie dough or wait to spread it on top of the baked cookies (or you can do both!). To add it to the dough, scoop 2 Tbsp of strawberry reduction to the top of the dough, then use a butter knife to gently marble the jam into the top of the dough.
Add 1/4 cup of granulated sugar to a shallow dish. Use a 3-tbsp cookie scoop to scoop the dough into balls (you should end up with about 16 cookies), then roll them in sugar until they're evenly coated. After you've scooped out half of the dough, marble another 1 Tbsp of strawberry reduction into the dough. Place the cookies about 3 inches apart on the prepared baking sheets.
Bake for 10-12 minutes, or until the edges of the cookies are set but the centers are still a bit soft. Cool for 15 minutes on the pan, then move the cookies to a wire rack to finish cooling. If you marbled the strawberry reduction into the dough, it can end up caramelizing at the edges of the cookies and stick to the parchment paper/silicone mats a bit. Once the cookies have cooled and solidified a bit, gently use a flat spatula or cookie lifter to gently separate any sticky bits without breaking the cookies.
If you want to spread any strawberry reduction on top of the cookies, do it right before you eat them. The reduction tastes amazing on top of them, but can make them get a bit soggy if you let them sit. These cookies can be stored in an airtight container at room temperature for up to 3 days.