This article by Shubert Spero may be helpful.
In terms of explaining this concept, which as you noted, is very much identified with R. J.B. Soloveitchik, Spero quotes the latter's Halakhic Mind (pp 101-102):
[T]here is only a single source from which a Jewish philosophical weltanschauung could emerge: the objective order - the Halakha ... Out of the sources of Halakha, a new world view awaits formulation.
He quotes Marvin Fox's summary of this position:
Religious and philosophical accounts of Jewish spirituality are sound and meaningful only to the extent that they derive from the Halakha. The deepest religious emotion, the subtlest theological understanding can only be Jewishly authentic to the extent that they arise from reflection on matters of Halakha.
Or R. Jonathan Sacks's take on R. Soloveitchik's position:
Halakha is the visible surface of a philosophy: the only philosophy that could legitimately claim to being Jewish.
However, as Spero notes, there were many giants who did not seem to believe that halacha can or must serve as the source for all Jewish philosophy:
If we examine the works of the classical Jewish philosophers - Sa'adya, Yehuda haLevi and Maimonides, we find that the prooftexts they offer are mainly from the Bible, and, if Rabbinic, are generally aggadic in nature. Even if one should disagree with some particular philosophic tenets of these thinkers, one cannot accuse all of them of having looked in the wrong place!