Like many of Robert Browning's wonderful poems, "Soliloquy of the Spanish Cloister" is a dramatic monologue--a kind of little play in verse. Biographical criticism, which depends on an understanding of the author's life, will not be as helpful in understanding the irony of this dramatic monologue as will historical criticism. The poem is set, as the title indicates, within a Spanish cloister in the Miidle Ages. The monks who lived there were believed to have dedicated their lives to God and have taken a vow of silence. The bitterness and resentment of the speaker indicates that he does not encompass the true meaning of charity, and we see in the poem a criticism of the hypocrisy of such an individual. The fuller your understanding of the Church in the Miiddle Ages, the more you will understand what is going on in the poem. Thus, historical criticism, which depends on understanding a work of literature in the context of its historical setting, will be more useful to you.
The poem also contains many religious and mythological allusions best understood within the context of historical criticism as well.