Returning to our specific case of, “[If he vows to bring] a small one and brings a large one, he fulfills his obligation”: When a person Vows to bring an offering, he is not promising to fulfill an individual mitzvah -- mystical meaning of “that which your lips give out (utter) heed,” to fulfill an individual mitzvah--, but rather, he is promising the all-encompassing concept of an offering, to offer himself to G-d, his entirety.
In the language of our sages (-Minochos 104b): Upon the unique wording of the verse (-Leviticus 2:1), “And a nefesh (lit. soul, meaning here, a person) when he brings a meal offering to the L-rd, his offering shall be of fine flour. He shall pour oil over it and place frankincense upon it,” our Sages explain, “For what (reason) is the meal-offering different (from other offerings in) that (the term) “a nefesh” is stated with regard to it? The Holy One, Blessed be He, said, ‘Whose practice (is it) to bring a meal-offering? (It is that of a) poor (individual; and) I will elevate (ascribe to) him as if he offered up his soul (nafsho) in front of Me.”
The words, “I will elevate him,” is that he will also have an empowerment from Above to “offer his soul”: ‘entirety’ to be more than what he accomplish in this from his own service, there comes that which, “G-d elevates upon him”
Thus, in his fulfilling this individual mitzvah --“that which your lips give out (utter) heed”-- of a voluntary offering, he becomes included within the all-encompassing mitzvah --mitzva is from the word tzavsa ‘bonding’-- the all-encompassing bond of a Jew --through a voluntary offering-- with G-d. Thus, here the primarily concern is the all-encompassing intent and concept --“and you shall do as you have promised”-- that which he is giving himself entirely, and thus becoming entirely closer, to G-d.
