I am usually pretty good at analyzing the grammar of sentences (I teach this very subject at least once a year!), but I have to admit that I am having a hard time with this sentence because of the words “proportional to” and the slash that you have placed between those words. I would be inclined to keep those words together, calling them a preposition. Here is how I would break up the sentence:
The hardness / of the peanut butter / is / proportional to / the softness / of the bread.
I am certain that “the hardness” is the subject and that “of the peanut butter” is a genitive construction (which is much like but not identical to the possessive) modifying “the hardness.” The main verb is “is”; the verb is in the present indicative, and it (the verb “be”) is likely to act as either a linking verb or an intransitive verb). So far, in other words, the sentence pattern is S V (or subject-verb).
“The softness” is just like “the hardness”; it is a noun phrase that is followed by a genitive construction (“of the bread”). That makes “the softness of the bread” a noun phrase.
I am inclined to see “proportional to” as a preposition, making “the softness of the bread” the object of the prepositional phrase, but I am less certain here.
In the end, I think that the sentence may be said to follow this pattern:
S – VI – Adverb
If so, the verb “is” must be acting as a intransitive verb (not a linking verb), and we have to accept that “proportional to the softness of the bread” is a prepositional phrase that functions as an adverb of manner (explaining how).
Maybe someone else can provide another way of analyzing the sentence.