Dilute the tomato sauce with the stock in a large pot and put it over low heat. Add half of the basil leaves, pepper, and salt, and keep the mixture warm (don’t let it boil).
Drizzle the olive oil in a large pan. Add the garlic and anchovies and, over very low heat, melt the anchovies completely in the oil. This takes about 2 minutes. I move the pan back and forth from the heat to avoid burning the garlic.
Once the anchovies are melted, remove the garlic, and add the rice. Toast the rice in the oil for about 2 minutes, until it is hot to the touch. Add the wine to deglaze the pan, stirring until the wine has evaporated and absorbed. Start pouring the diluted tomato sauce into the pan a little at a time. Make sure to stir the rice frequently and always wait for the liquid to evaporate almost completely before adding more.
After 30 to 35 minutes of stirring occasionally, the rice should be soft. Add the butter, capers, and olives, and turn off the heat. Stir the mixture vigorously to melt the butter with the residual heat. This gives the risotto a creamy consistency. Cover the pan and let the risotto rest for 5 minutes.
Serve the risotto with the remaining basil on top.