Combine the ground beef with the cheddar cheese and jalapeno slices in a large mixing bowl. Season with salt and pepper to taste. Form ¼ pound each burger patties.
Over high heat place a grill plate and when hot brush some oil over the surface.
Add the burger patties and cook to desired doneness paying attention as the cheese will melt and stick to the grill. 4 to 5 minutes per side.
On a plate place a small bed of spinach and add the burger on top of it. Add the radishes and limes with avocado to your plate.
Giangi's Kitchen provides nutritional information, but these figures should be considered estimates, as a registered dietician does not calculate them.