The forms reverted to brest- in Middle English from influence of Old Norse brestan/brast/brosten, from the same Germanic root, but it was re-metathesized late 16c. and emerged in the modern form, though brast was common as past tense through 17c. and survives in dialect.
In Old English "Chiefly said of things possessing considerable capacity for resistance and breaking with loud noise; often of cords, etc., snapping under tension; also of spears, swords, etc., shivered in battle" [OED]; in late Old English also "break violently open as an effect of internal forces." Figuratively, in reference to being over-full of excitement, anticipation, emotion, etc., from c. 1200. Transitive sense ("to cause to break, cause to explode") is from late 13c. Meaning "to issue suddenly and abundantly" is from c. 1300 (literal), mid-13c. (figurative). Meaning "break (into) sudden activity or expression" is from late 14c. Related: Bursting.
derivational suffix, also -le, used mostly with verbs but originally also with nouns, "often denoting diminutive, repetitive, or intensive actions or events" [The Middle English Compendium], from Old English. Compare brastlian alongside berstan (see burst); nestlian (see nestle) alongside nistan). It is likely also in wrestle, trample, draggle, struggle, twinkle, also noddle "to make frequent nods" (1733). New formations in Middle English might be native formations (jostle from joust) with this or borrowings from Dutch.