Peel the cucumbers and use a spoon or sharp knife to remove the seeds. Cut the cucumber flesh into batons approximately 1/2 inch wide by 2 inches long. Place the batons in a bowl with the vinegar, salt, and sugar. Transfer the cucumbers to a large colander to drain for at least 30 minutes or up to one hour.
As the time for the cucumbers to drain comes to an end, preheat the oven to 375 degrees Fahrenheit. Coarsely chop the fresh herbs. Melt the butter and set aside as you prepare the cucumbers.
Transfer the drained cucumbers to a clean kitchen towel. Gently pat dry to remove as much moisture as possible. Transfer the cucumbers to a casserole dish large enough to allow the cucumbers to bake in a single layer. Add the melted butter and toss gently to coat. Sprinkle with the fresh herbs and add freshly ground black pepper to taste.
Bake the cucumbers in the preheated oven for approximately one hour, tossing once or twice during baking. The cucumbers should be tender, but still al dente when finished with just a hint of brown color.
Remove the cucumbers from the oven. Taste for seasoning, adding more salt or pepper if desired. Serve warm.