Is it possible to use verbs after verbs with prepositions?
For example: Ich denke an essen.
Or does this kind of sentence has to be made with nouns?
For example: Ich denke an das Essen.
Well, yes and no.
It is possible, but in this case the verb is considered a noun (substantiviert in German) and therefore capitalized even if there is no article:
Ich denke an Essen.
This is unusual (normally one would use an Article and write Ich denke ans Essen) but valid. Because of the capitalization it is impossible to distinguish das Essen (the meal) from the substantivated verb essen (to eat).
Usually, infinitives used as nouns are preceded by an article, but this doesn't have to be always the case. Another example:
Zu schnelles Fahren ist verboten.
Note that infinitives following zu are a special case because an infinitive after zu is still a verb: Es ist verboten zu rauchen.
There are ambiguous cases where an infinitve can be considered a verb or a noun, as in:
Rad fahren ist verboten.
Radfahren ist verboten.
which is both valid, but here we have no preposition.
Yes it's possible even though it may appear strange or incomplete. But it is used in german language.
Your examples describe something different, which indicates both versions have a reason to be used.
Edit: Now that RHa's answer has arrived I assume the form "think about the procedure of eating" is the substantivated verb and should be capitalized. I must admit I am not sure how to write this correctly.