Brochas: Daf Lamed Ches amud beis

And the law is (we recite) "HaMotzi Lechem Min haAretz (rather than "Motzi" without the preceding article - "heh") for we hold in accordance with the Rabbis who say that ("HaMotzi" also) connotes the One who has brought forth (from Mitzrayim.)

Tosfos, based on a Yerushalmi, explain that the interposition of the letter "heh" prevents consecutive use of the letter "mem" at the end of "Olam" and beginning of "Motzi."  The Ben haYehoyada cites Tosfos and then briefly elaborates that the "hey" itself has significance on the basis of two "kavonos" elaborated by the Ari in his sefer Shaar haMitzvos daf 54

The two kavonos concern the two letters Heh in the Tetragrammaton (shem Havayah). These are Midos of Hashem. The first Heh = Ima Bina; the second Heh = Malchus. The first Heh represents the mother giving birth to existence; the second Heh represents existence in its finality (i.e. completeness).

So the two Kavonos when saying HaMotzi are:

1.       Heh Motzi = Ima Bina the source of existence and of sustenance.

2.       Heh Motzi = Malchus the completeness of that existence

On eating bread one recognises both source and completeness.

The two "Hehin" are the same letter, because the ultimate purpose of existence is to match the final outcome to the original intention – sof maaseh bemachshovo techila.