。
She speaks English as well as I do.
Literal
She [topic-は] me [as-と] same-amount well English [object-を] speaks.
X と同じくらい~ ('as ~ as X') is the equal-comparison frame, but here the dimension being compared is the manner of an action rather than a fixed property. よく functions adverbially on 話す ('speaks well'), and と同じくらい modifies that adverb — 'speaks well to the same degree as me.' Adverbs of degree happily nest inside the comparison. The unspoken implication is that the speaker considers themselves a competent English speaker; the comparison flatters her by matching that level.