How do I clean deep burns in my oven?
I trust you've already tried leaving a hot, wet (just water) cloth on it for a while, which may work if its sugar, as opposed to grease.

As long as your oven manual allows (it typically will, unless its a self-cleaning or continuous-cleaning oven), oven cleaner, which is basically caustics such as lye and solvents. Easy-off is a common brand in the US. Note, BTW, oven cleaner is one of the products where you actually want to read and beware the cautions on the side of the can.

Also, unless you actually see the black stuff on the bottom smoking, I'd guess its more likely to be the brown stuff everywhere else.