In a 4- to 5-quart pan, combine onion and 1/4 cup water. Bring to a boil over medium-high heat; then boil, stirring occasionally, until liquid evaporates and onion begins to brown (about 5 minutes). To deglaze, add 1/4 cup more water and stir to scrape browned bits free. Then continue to cook, stirring occasionally, until onion begins to brown again. Repeat deglazing and browning steps, using 1/4 cup more water.
Crumble turkey into pan; add garlic. Cook, stirring, until meat is no longer pink and liquid has evaporated. Stir in tomato sauce, tomatoes, beans, molasses, hot pepper seasoning, cocoa, paprika, cumin, oregano, and basil. Bring to a boil; reduce heat, cover, and simmer until flavors are well blended (about 30 minutes).