In a food processor, combine butter, olives, shallot, and garlic. Pulse to combine and set aside.
To make the green beans:
If using a smaller pot, you may have to blanch the green beans in batches. Set out a large bowl of ice water before blanching the beans.
In a large saucepan or stock pot, bring 4 quarts water and 1 tablespoon salt to boil.
Add the green beans and boil until tender-crisp, but still bright green, about 3 to 5 minutes. Drain well and immediately plunge into ice water to stop the cooking.
In a large skillet, add 1/4 cup water over medium heat. Add blanched beans and toss until heated through.
Add olive butter and toss with the beans until the butter coats the beans (but you don't want it to melt into a puddle). Season to taste with salt and pepper (but remember the olives are already salty). Transfer to a serving platter and serve.
To trim the beans, snap or cut off the stem ends and remove any strings along the length of the beans. Leave the tails attached.