Looking for more than a "measure of sanctity"

From Rabbi Rosensweig's essay, "The Spiritual Legacy of Noah and Avraham":

These two perspectives [Noah's and Abraham's] are reflected in the contrast between the full complement of halakhic obligation and the Noahide code. The 613 commandments relate to and regulate every dimension of human life, expanding the concept and scope of the sacred and suffusing the mundane with sancitiy. The more limited seven-obligation Noahide code does effectively insure significant social stability, a standard of monotheism, as well as a measure of sanctity in other realms of life, but it does not approximate the pervasive and ambitious program of the halakhah.

In reading these words, I had to ask myself what then does the Jewish tradition claim a ben Noach should do if they want more "measure of sanctity"? Where and how can one find it and strive with Abraham for something more, something like Rabbi Soloveitchik describes in this passage from Out of the Whirlwind (p. 171), which I find as one of the most moving and important passages in all of Rabbi Soloveitchik's writings.

The way of every Jew to God must not differ from the trail along which Abraham moved toward his destiny, which had to be blazed through the wilderness of a brute and nonsensical existence. The experience is attained at the cost of doubts and a restless life, searching and examining, striving and pursuing—and not finding; of frustrating efforts and almost hopeless waiting; of grappling with oneself and everybody else; of exploring a starlit and moonlit sky and watching the majesty of sunsets and sunrises, the beauty of birth and also the ugliness of death and destruction; of trying to penetrate behind the mechanical surface of the cosmic occurrence and failing to discover any intelligible order in this drama; of winning and losing and reaching out again; of being able to put on a repeat performance of something which I had and lost; of asking questions and not finding answers; of ascending the high mount like Moses and falling back into the abyss, shattering everything one has received, and yet pulling oneself out of the depths of misery and trying to climb up the mountain again with two new stone tablets.