How can I cheaply cook a bratwurst that is similar to a grilled brat with only access to an oven or stovetop?
Most ovens have a 'broil' setting (where the top element is on, and not the lower element).

You'll likely want a 'broiler pan' so that you can drain the grease away from the food (and catch it so it doesn't light on fire).  They're under $20 online.


Set the rack of the oven so that the food will be about 2" from the upper heating element.
Heat the broiler on its hottest setting, but leave the door to the oven open.
Place the food in the oven, but again, don't close it.
Turn the food occasionally until it's cooked to the level you want.


As for the bit about not closing the door : 
If you close the door to the oven, it might heat up too much, and shut off.  You need the element actively heating, so that you have radiant heating, not convection or conduction.  (this is also why you want the food really close to the heating element).  Note that this is for electric ovens -- I don't think gas ovens have the same issue.