In a medium bowl, combine flour, 2/3 cup of the sugar, and salt. Whisk to combine.
Add the butter and use your fingertips to rub the butter into the flour mixture until the mixture sticks together in clumps.
Mix in the oats.
This is a great step to do ahead of time. In fact, it's best to do it ahead of time. Try to make it the day before and refrigerate it covered well. At the very least, try to make the crumble topping a couple hours before you bake the crumble so it has time to chill in the refrigerator.
Preheat oven to 375°F. Spray a 11x7x2-inch (or about that size) glass baking dish with non-stick spray.
Add remaining 1/2 cup sugar and the vanilla bean paste in a large bowl. Mix well.
Add the strawberries and the rhubarb to the sugar mixture and toss to coat well.
Pour the fruit filling into prepared baking dish. Sprinkle oat topping evenly over filling.
Bake the crumble until filling bubbles thickly and topping is crisp, about 45 minutes. Let cool 15 minutes. Spoon warm crumble into bowls. Serve with buttermilk whipped cream.