Preheat oven to 375°F. Toss rhubarb, strawberries, honey, and vinegar on a rimmed baking sheet; spread in a single layer. Bake 25 to 30 minutes or until fruit is soft, stirring occasionally.
Add fruit to a high-speed blender, and puree until smooth. Cover and chill. Meanwhile, whisk egg yolks and cornstarch in a large heat-proof bowl; set aside.
Combine milk and sugar in a small saucepan. Cook over medium-low heat 5 to 10 minutes or until sugar dissolves. Gradually pour milk mixture into egg yolks, whisking constantly.
Add mixture back to saucepan; cook over low heat, stirring constantly, until mixture is thick and coats the back of a spoon. Pour egg mixture through a sieve into cream; whisk to combine.
Whisk in rhubarb-strawberry puree, vanilla, and 1/4 tsp salt. Chill 1 to 2 hours or overnight.
Meanwhile, combine flour, brown sugar, 1/2 tsp salt, and butter in a large bowl; stir until mixture resembles coarse sand. Stir in oats; spread mixture on a large rimmed baking sheet. Bake 20 to 25 minutes or until golden brown; cool.
Pour custard into container of an electric ice cream freezer; freeze according to manufacturer's directions. Add baked crumble mixture during last 5 minutes of freezing. Spoon ice cream into a freezer-safe container; freeze up to 1 month.