Break garlic cloves off the bulb, but leaving in the peels. Place cloves in a square of foil. Drizzle about 1 tablespoon olive oil over cloves; season with salt and black pepper. Fold foil into a packet with the seams facing up to avoid leakage.
Bake in the preheated oven, checking every 10 to 15 minutes, until garlic is soft, 30 to 40 minutes. Let cool.
Heat walnuts in a skillet over medium heat; cook and stir constantly until fragrant and toasted, about 5 minutes. Remove from heat and cool.
Bring a large pot of lightly salted water to a boil. Pour ice water in a large bowl and set aside. Drop a handful of basil into the boiling water for 2 seconds; remove with a slotted spoon and transfer to the ice water. Repeat with remaining basil. Drain basil from the ice water and squeeze out as much moisture as possible.
Squeeze garlic to release from the peels and place in a food processor. Add toasted walnuts, basil, and 1 cup olive oil; season with salt and black pepper. Blend in the food processor, scraping sides a few times, until smooth.
Pour pesto into 1 to 2 ice cube trays; freeze until completely solid, 8 hours or overnight. Pry pesto cubes from the ice cube tray and store in a freezer bag.
