Slice sirloin into about 1/4 inch strips (cutting against the grain to make the steak more tender!). Season liberally with salt and pepper. In a grill pan, coat with some vegetable oil. When the pan is hot, add the steak (work in batches as not to overcrowd the pan). Cook for about 2 minutes on each side. Let the steak rest for a few minutes.
To assemble the sliders, add a few slices of steak and top with the tzatziki sauce and some of the sliced red cabbage.
Peel cucumbers and cut in half longways. Using a spoon, remove the seeds from the inside. Grate the cucumbers on the largest holes of a box grater into a mixing bowl. Remove excess water from the cucumbers using a paper towel and pressing lightly on the shredded cucumbers.
In a mixing bowl, combine yogurt, lemon juice, cucumbers, dill, and season with salt and pepper.