In a 2- to 3-quart pan over high heat, bring 6 1/2 cups broth to a simmer; cover and reduce heat to maintain simmer.
Meanwhile, in a food processor, whirl basil, garlic, and 1 teaspoon olive oil until coarsely chopped. Add cheese and whirl until finely ground.
Add remaining 2 teaspoons oil and the butter to a 5- to 6-quart pan over medium-high heat; when hot (mixture will be foamy), add shallots and stir often until limp, 1 to 2 minutes. Add rice and stir often until beginning to turn opaque, 1 to 2 minutes.
Add wine and stir until absorbed, about 1 minute. Add 6 cups broth, 1 cup at a time, stirring after each addition until almost absorbed, 25 to 30 minutes total. Stir in basil mixture and cook, stirring often, until rice is barely tender to bite and mixture is creamy, about 2 minutes longer. If risotto is thicker than desired, stir in a little more broth.
Ladle risotto into wide, shallow bowls, and serve immediately.