Preheat oven to 350 degrees. Butter a 9x13 baking dish or individual ramekins.
Measure sugar into a mixing bowl. Add the lemon zest, then use a fork to moosh them together. Stir in the corn starch, then add the blackberries and combine well. Pour the blackberries into your prepared baking dish or ramekin.
Combine flour, brown sugar, and oats in a large mixing bowl. Cut the butter in until the mixture is combined and in little crumbles. It's easiest to do when the butter isn't super soft--room temperature or just a bit cooler works best.
Cover the blackberries with the crumbly topping, then bake for about 45 minutes or until golden brown and bubbly. NOTE: My oven cooks fast I've discovered, so I start with 35 minutes and go from there. But I've had other ovens that took the full 45 minutes!*See recipe notes for the recipe that serves 2.
Notes
RECIPE FOR 2:1-1/2 c. Blackberries 1 T. sugar 1/2 tsp. cornstarch 2 tsp. Lemon zest 1/4 c. flour 1/4 c. oats 3 T. Brown sugar 2 T. ButterFollow the same directions as above. I used a 16 oz. ramekin and it came up 2/3 up to the top. You could use more fruit if you like, or up the ingredients, using the same proportions. You could also use two 8 oz. ramekins instead.