Heat butter in a small saucepan over medium-low heat until it smells nutty and brown bits form on the bottom, 15 to 17 minutes. Don't crank up the heat to try to get there faster; you'll just end up with burned butter.

Meanwhile, pulse together graham crackers, brown sugar, and salt in a food processor until fine crumbs form. Carefully pour butter into crumb mixture while food processor is running. Press combined mixture into bottom and sides of a 10-inch tart pan with a removable bottom. Chill for 1 hour or freeze for 20 minutes until set.

Stir together gelatin and cold water in a small bowl. Let stand for 5 minutes, then microwave until gelatin dissolves, about 10 seconds.

Beat cream cheese in a bowl with an electric mixer for 30 seconds. Add yogurt, white sugar, lemon juice, lemon zest, salt, and vanilla. Beat until smooth, then beat in gelatin. Pour mixture into the chilled crust. Chill until set, about 2 hours.

Stir together blueberries, brown sugar, poppy seeds, lemon juice, and lemon zest. Scatter topping over cheesecake.