Peel the cucumbers. Cut in half lengthwise and scoop out the seeds with a spoon. Cut into lengthwise strips about 3/8 inch wide. Cut the strips into 2 inch pieces.
Toss the cucumbers in a 2 1/2 -quart porcelain or stainless steel bowl with the vinegar, salt, and sugar. Let stand for at least 30 minutes or for up to several hours. Drain. Pat dry in a towel.
Preheat oven to 375 degrees.
In a baking dish 12 inches in diameter and 1 1/2 inches deep, toss the cucumbers with the butter, herbs, scallions, and pepper. Set uncovered in middle level of the preheated oven for about 1 hour, tossing 2 or 3 times, until cucumbers are tender but still have a suggestion of crispness and texture. They will barely color during the cooking.
If the natural moisture content is not withdrawn beforehand, cucumbers exude so much water as they are heated that you usually end up with a tasteless mush. Blanching for 5 minutes before cooking will remove unwanted water, but also most of the cucumber flavor. A preliminary sojourn in salt draws out the water yet leaves the flavor, which a little vinegar and a pinch of sugar accentuates. Baked cucumbers go well with roast, broiled, or sauteed chicken and sweetbreads.