Make the blueberry swirl: In a small saucepan, combine blueberries, 3 tbsp sugar, lemon juice, and cornstarch. Cook over medium heat, stirring and lightly smashing berries, until thick and glossy, 8–12 minutes. Scrape onto a plate to cool completely.
Cheesecake centers: Beat the cold cream cheese with powdered sugar and 1/4 tsp vanilla until smooth and fluffy, about 1–2 minutes. Drop 18 heaping 2-teaspoon mounds onto a parchment-lined small tray and freeze until firm, 30–45 minutes.
Dry ingredients: Whisk flour, baking powder, baking soda, and salt in a medium bowl; set aside.
Flavor the sugar: In a large bowl, rub the lemon zest into 3/4 cup sugar with your fingertips until fragrant and slightly damp. Add the very soft butter and beat on medium-high until light and creamy, 1–2 minutes.
Mix the dough: Beat in the egg and 1 1/2 tsp vanilla until pale and fluffy, about 1 minute. Add the dry ingredients and mix on low just until no dry spots remain. Fold in white chocolate chips if using. Cover and refrigerate the dough for 20 minutes to firm slightly.
Swirl in the jam (no overmixing): Turn the chilled dough onto a sheet of parchment and pat into a rough 10×8-inch rectangle. Spoon several small dollops of cooled blueberry jam (about 1/2 cup total) over the surface. Fold the dough over itself like a letter, rotate, and fold once more until streaks of jam run through the dough. Do not fully blend.
Preheat the oven to 375°F. Line two large baking sheets with parchment paper.
Shape: Scoop 2-tablespoon portions of dough. Flatten each in your palm, place a frozen cheesecake mound in the center, and wrap the dough fully around it. Gently press into a thick disc about 2 inches wide. Sprinkle tops with coarse sparkling sugar if using. Keep remaining cheesecake mounds frozen until needed.
Bake: Arrange 6–8 cookies per sheet and bake 10–12 minutes, until edges look set and the centers are just matte. Tap the pan once on the counter right out of the oven to settle the centers. Cool on the sheet for 5 minutes, then move to a rack to finish cooling so the filling sets.