Combine the ground beef, grated onion, yoghurt, garlic powder, cumin, oregano, paprika, cayenne, black pepper and salt in a bowl. Mix very well until the mixture is completely uniform.
Divide the mixture into two portions. Place one portion in the middle of a sheet of parchment paper, cover with a second sheet, and press it into a thin, even rectangle. I used a rolling pin but your hands or a long glass work too. Repeat with the second portion.
Fold the parchment over the meat repeatedly, rolling it into a long, flat rope shape. Place the wrapped meat on a baking tray.
Unroll or slice the cooked meat and break it into thin pieces.
Squeeze over a little lemon juice. If you like it crispier, return it to the oven for 5 minutes.
Make the tahini sauce by whisking the tahini, lemon juice, grated garlic, yogurt and salt, adding water gradually until the sauce becomes creamy and pourable.
Warm the pitas.
Assemble the doner by adding the cooked beef, tomatoes, jalapeños, tahini sauce and any extras you love. Fold or wrap and enjoy immediately.