Preheat the oven to 350°F (175°C). Grease a 9x13 inch baking dish with butter or non-stick spray.
Slice fresh rhubarb stalks into 1/2-inch pieces and place them evenly in the prepared baking dish. Sprinkle 3/4 cup sugar and 2 tablespoons flour over the rhubarb, then add 1 teaspoon vanilla extract. Toss gently to coat the fruit evenly.
In a mixing bowl, combine rolled oats, 1 cup flour, brown sugar, and melted butter. Use a pastry cutter or fork to blend until the mixture forms coarse crumbs with some small clusters.
Evenly sprinkle the crumb topping over the rhubarb filling, ensuring all the fruit is covered.
Bake in the preheated oven for 40-45 minutes, or until the topping is golden brown and the filling is bubbling around the edges. Listen for a gentle sizzle and watch for a deep golden color on top.
Remove from oven and let cool slightly before serving. The crisp should have a fragrant aroma and a crispy, crunchy topping with tender, vibrant rhubarb underneath.