The rule you were taught is an over-generalization. The sentence written above is correct with no commas at all. The "rule" about especially only applies to the case when especially is being used as a parenthetical phrase, usually at the end of a sentence.
We really like ice cream, especially chocolate ice cream.
This rule is not unique to the word especially, but is used for all sorts of sentence-final parentheticals:
The "rule" about especially only applies to the case when especially is being used as a parenthetical phrase, usually at the end of a sentence.
Since your sentence is not using especially to begin a parenthetical statement, it does not require a comma. It is, however, stylistically awkward, and I would recommend the following revision:
Secondary electron emission from metallic surfaces, especially dielectric surfaces, is a fundamental process of great technological significance