Put the jasmine rice, 2 1/4 cups water, and 1/2 teaspoon of the kosher salt into a medium saucepan. Set the saucepan over high heat and bring the water to a boil.

Cover the saucepan, turn the heat down to low, and cook the rice for 15 minutes. When the time is up, take the saucepan off the heat and let it sit, covered, for 5 minutes.

While the rice cooks, fill a small saucepan with water and bring it to a boil over high heat for the eggs.

Carefully lower the eggs into the boiling water. Cook them for 7 minutes, which gives you yolks that are set around the edges and still a little soft in the center.

Lift the eggs out of the saucepan and transfer them to a bowl of cold water so they stop cooking. Set the bowl aside.

Put the drained butter beans into a colander if you have not already. Rinse them under cold water and let them drain well.

Finely grate the zest from the lemon into a small bowl. Squeeze 1 tablespoon of lemon juice into the same bowl, then cut the rest of the lemon into wedges for serving.

Set a large skillet over medium-high heat and add the olive oil. When the oil looks shiny, add the green beans and the remaining 1/4 teaspoon kosher salt.

Cook the green beans in the skillet for 4 to 5 minutes, stirring every minute or so, until they turn bright green and pick up browned spots.

Keep cooking the green beans for 2 to 3 more minutes, stirring again, until they are tender but still a little firm in the middle.

Add the butter beans to the skillet with the green beans. Sprinkle in the black pepper and add 2 tablespoons of water, then cook for 2 to 3 minutes, stirring gently, until the beans are hot and the water is mostly gone.

Add the basil pesto to the small bowl with the lemon zest and lemon juice. Stir in 1 tablespoon of water so the pesto loosens enough to spoon over the bowls.