Q. For 20 years, I have said Hallel on Rosh Chodesh without a bracha because I heard this is the way the Brisker Rav did it. Should I change my minhag?

A. Rambam (H. Chanuka 3: 7) maintains that you recite Hallel on Rosh Chodesh without saying a brocho, since it is only a minhag and you do not recite a brocho on a minhag. His opinion is quoted in Shulchan Aruch (O.H. 422: 2), where another opinion (Rif and Rabbenu Yona) that differentiates between Hallel recited by an individual or a tzibur is also mentioned. However, Remoh (ibid.) rules like Rabbenu Tam and the Rosh that we do recite a brocho on Halel, since on many minhogim such as Yom Tov Sheni, we also say blessings. (See Tosafos Brochos 14a d.h. Yomim)
The Brisker Rov zt”l explains that the Rambam understands the brocho on Hallel as being a common brocho on a mitzva. Therefore, when Hallel is recited only as a minhag, as in Rosh Chodesh, it looses the brocho. On the other side Rosh and Tosafos maintain that Hallel is a cheftza or an article of mitzva itself, and even when it is only a minhag to be recited, it still requires a brocho. He compares Halel to how his father, Hagrach zt”l explained the brocho on learning Torah, namely that the cheftza of Torah requires a brocho.
The minhag of Brisk may be not to say a brocho on the Halel of Rosh Chodesh, following the Rambam’s opinion. People who davened there relate that the chazzan said Hallel with a brocho and was motzi Horav Velvel Soloveitchik (Horav Dovid’s son the Brisker Rav’s grandson) with that brocho.
However, Remo and Mishan Berura (ibid.) rule that the tradition of Askenazim is to recite Hallel with a brocho, although it is better, when possible to say it together with a tzibur.
Horav Shlomo Miller’s Shlit”a opinion is that a person should maintain the inherited traditions of his family and the community he belongs to.

Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit’a