Preheat the oven to 350°F (175°C) and line a baking sheet with parchment paper.
Melt the 2 sticks of salted butter in a skillet over medium heat and cook until it begins to lightly brown, about 2 minutes; remove from heat and transfer to a mixing bowl. Let cool about 5 minutes.
Stir the 2/3 cup brown sugar, 1/3 cup granulated sugar, eggs, and 1 tablespoon vanilla into the cooled brown butter until smooth.
Add 2 1/4 cups all-purpose flour, 1 teaspoon baking soda, and 1/2 teaspoon kosher salt to the wet mixture and stir until just combined.
Gently fold in 2 tablespoons blueberry jam and 3/4 cup fresh blueberries, swirling the jam so it remains streaky rather than fully mixed into the dough.
Make the streusel by combining 1/3 cup flour, 1/4 cup packed brown sugar, 1/2 teaspoon cinnamon, and 3 tablespoons cold cubed or grated butter; rub together with your fingers until crumbly.
Roll the dough into rounded tablespoon-size balls and place them about 2 inches apart on the prepared baking sheet. Gently flatten each ball slightly.
Sprinkle about 1 tablespoon of streusel over each cookie, then bake for 8 minutes. Remove the baking sheet, rotate it, and tap it on the counter 1–2 times to help flatten the cookies.
Return the baking sheet to the oven and bake another 3–4 minutes, until the cookies are just beginning to set around the edges.
Let the cookies cool on the baking sheet; they will continue to set as they rest. Serve warm or at room temperature.