Pfeffernusse
I like it. You mention that it bloomed once and has not since. It's not a sempervivum as the rosette dies after blooming. I agree with Bev that it most likely is an echeveria. The growth may not be typical of an echeveria grown in strong light, I find the form of your plant pleasantly attractive and unique. I disagree with your assessment that you haven't cared for it properly and that it's weird. Evidently it's your care that has acclimated your plant to grow well in less than ideal conditions. I see lots of healthy looking leaves, all of equal size and shape, with a full, compact growing tip. Typically a high light plant such as this would have a long, lanky growing tip reaching for more light, with few if any healthy leaves below. I personally would not change a thing about how you've been growing it. Myself, I would like to see just how long I could grow this and keep it relatively healthy, even though the stem may eventually be exposed. I find it fascinating that you've kept this looking so healthy.
If it were mine, I would carefully remove the dead leaves at the base. Start nearest the soil, using tweezers detach each dead leaf as you go around the plant. Once all the dead leaves are removed, I would carefully remove the bottom row of healthy leaves for propagation. I like to grasp the lowest leaf near the mid point, being careful not to crush it. I then move the entire leaf to one side and wait for a "pop" as that side of the leaf detaches from the stem. I then move in the opposite direction until the leaf pulls free. Ideally the entire leaf detaches from the stem. Sometimes the leaf might break leaving a small bit attached to the stem. Some growers cut the leaves off with scissors or a sharp knife. In my experience fully detached leaves tend to root faster and produce new plantlets sooner than broken or cut leaves. Those can still produce roots and new plants, it just seems that it takes them longer. I place each leaf on an individual 2 1/2" nursery pot full of soil and top dressed with a thin layer of fine gravel. It's been my experience that leaves laid directly on the soil can sometimes develop a fungus and eventually rot away. The gravel still allows for good root development with less risk of fungal development. Once the roots start to grow, I don't like to disturb them. Changes in conditions can lead to a transplant shock, slowing further growth. Instead I let the roots grow down through the gravel into the soil. A healthy rosette will soon appear and typically as the rosette grows the parent leaf tends to die back, although not always. I have had instances where the leaf continued to grow along with the rosette. These I remove the leaf with a sharp knife. Once the rosette begins to develop I move it into stronger light slowly acclimating it until it can take full on bright light.