Eastern Sefardim don’t say a beracha on half hallel. Western Sefardim say Ligmor Et Hahallel on whole hallel, and Likro Et Hahallel on half hallel.
Shearith Israel, the oldest kehilla in America, says “1/4 hallel” on Thanksgiving, starting from Hallelu Et Hashem Kol Goyim. Obviously without a beracha. But today of course they said half hallel with a beracha.