μὲν οὖν is a combo: “Well, yes."
And ὃ ἐπαγγέλλομαι amplifies τὸ ἐπάγγελμα, lit. “the promise that I promise,” cognate accusative.
It’s not a strange sentence in Greek.
“Why, yes! This is the very (αὐτὸ) promise that I make” or “That is precisely what I profess.”