Preheat oven to 350F. Line a baking sheet w/ parchment paper.
Brambleberry Sauce: Add the berries, sugar & lemon juice to a saucepan over medium-high heat. Mix & bring to a boil for 5-7 mins, stirring occasionally. Once berries soften & have released their juices, gently smash.
Pour the slurry into the berry sauce mixture; mix. Cook for another 2-3 mins, until thickened. Remove & place in a bowl. Chill completely in fridge.
Baked Crumble: In a medium bowl, combine all of the ingredients. Mix w/ a fork until crumbly.
Spread mixture across the baking sheet. Bake @350F for 10-15 mins, until golden & crispy.
Remove & cool for 10 mins. Then break it apart into crumbles. Set aside.
Ice Cream: In a large bowl whisk together the sweetened condensed milk, vanilla & salt until well combined.
In the bowl of a stand mixer w/ whisk attachment (or a handheld electric mixer), beat the cream cheese to smooth. Add the heavy cream & beat 3-4 mins, until stiff peaks form.
Add the whipped cream mixture to the sweetened condensed milk mixture; gently fold until fully combined.
Assemble: Pour ⅓ of the ice cream mixture into a 9x5" loaf pan that's lined w/ parchment paper. Dollop 2-4 tbsp of the brambleberry sauce all over, followed by a generous sprinkle of crumble. Repeat this process 2 more times. Use a knife to gently swirl.
Cover pan w/ a lid or foil; freeze for at least 6 hrs or overnight.
Scoop & serve the ice cream w/ a drizzle of olive oil & sprinkle of flaky sea salt, if desired.
