Combine chicken broth, chives, roasted garlic, and basil in a saucepan; bring to a boil. Reduce heat and simmer.
Heat vegetable oil and butter in a separate pot over medium heat; cook and stir shallot and garlic in the hot oil-butter mixture until shallot is softened, about 5 minutes.
Add rice to shallot mixture; increase heat to medium-high. Cook and stir until rice is fragrant, about 2 minutes.
Add wine, reduce heat to low, and simmer until wine is absorbed, about 5 minutes.
Stir simmering broth mixture, 1/2 cup at a time, into rice mixture and continue to simmer until rice absorbs liquid; repeat, adding 1/2 cup of broth at a time, until all the broth is absorbed and rice is tender, 20 to 25 minutes. Stir half-and-half into risotto; fold in Gorgonzola cheese until melted.