Make the compote: Sterilize 2 pint jars. Combine blueberries, lime juice, and 2 cups of sugar in a medium saucepan. Heat over a medium flame until the blueberries liquefy and their juices turn syrupy. Stir and remove from heat. Spoon the mixture into the jars, tighten the lids, and flip upside-down until room temp. Keep refrigerated.
Make the streusel:Using your fingers or a food processor, combine the flour, ¼ cup sugar, cinnamon, and a pinch of salt, then mix in 2 ounces butter until crumbly. Spread mixture onto a parchment-lined baking sheet and bake at 350 F for 10 minutes. Using a fork, stir the streusel up, then bake for another 10 minutes or until golden brown. Crumble up and let cool.
Make the ice cream:Melt 4 ounces butter over medium heat until takes on a nice golden brown color. Remove from heat and allow to cool to room temperature. Place 3 cups half and half in a large pot over medium high heat and and cook until nearly boiling. Meanwhile, whisk together the yolks, sugars and salt until smooth. To temper the egg mixture, carefully whisk in about 1 cup of the hot half and half into the egg mixture until smooth. Then whisk the egg mixture into the remaining amount of half and half in the pot. Return to medium low heat, and cook up to 170 degrees F, stirring constantly to ensure even cooking. When the mixture reaches 170, remove it from heat and whisk in the vanilla and browned butter. Strain mixture through a wire mesh strainer into a large bowl. Cover with plastic wrap and place in refrigerator until completely cool.
Once the mixture is chilled, pour it into an ice cream maker and process according to the manufacturers instructions. Transfer ice cream to a large container and fold in 1/4 cup blueberry compote and 3 tablespoons cinnamon streusel. Cover and freeze for at least 2 hours until firm.