Mix the sea salt, vinegar and water in a large saucepan and bring to a boil. Reduce the heat and simmer for 5 minutes. Remove the brine from the heat and allow it to cool slightly. Arrange the cucumbers upright in 2 quart-size jars. Add the dill sprigs and sliced peppers to the jars. The cucumbers should fit tightly and should come within 1/2 inch of the top of the container.
Fill the containers with the brine to the top and tap on a flat surface to remove any possible air bubbles. Cover and refrigerate until pickled and chilled, at least 6 hours but preferably overnight. The pickles will last in the refrigerator for up to a few weeks.