Make the oil: In a food processor, combine chives, cilantro and basil, and pulse until finely chopped. Add olive oil, and pulse again until mixture is silky and emulsified. Transfer to a small bowl, stir in lemon juice and salt to taste. Set aside.
Prepare the beans: In a 10-inch skillet, heat olive oil over medium-low heat. Add garlic and cook until translucent, about 1 minute. Add beans to the skillet and season with salt and pepper. Cook, stirring occasionally, until the flavors have melded, about 2 to 3 minutes. With the back of a spoon or spatula, smash about ⅓ to ½ cup of the beans and stir until they are incorporated into the rest of the bean mixture. A good portion of the remaining beans should maintain their structure.
Add stock or water and bring to a gentle simmer. Cook until sauce becomes creamy and is reduced by about about half, about 1 to 2 minutes more. Smash additional beans and add a few more tablespoons of water, if needed, to reach desired consistency and stir again to combined.
Transfer beans to a bowl and swirl with herb oil on top. Season with flaky salt, if desired.