For the specific use case of cooking, I think the problem you will run into is that solar power is inconsistent which is problematic for cooking via direct heat as you tend to need consistent temperatures.

So instead I would look at indirect heat. By super-concentrating the full parabolic area into a single point, you can heat cooking stones which will radiate heat more consistently even when clouds momentarily block the sun.

Using a simple store-bought pizza stone suspended at a 45-degree angle above your food, the homemade solar "laser" (said in Dr. Evil's voice) could be targeted on the underside, directly above the food.

Placing firebrick or other insulating stone directly on the opposite side of the pizza stone would help ensure that minimal energy is lost through the rear.