Working with 1 cucumber piece at a time, stand piece on its end and make 1 deep vertical cut roughly three-quarters of the way to the bottom; make another, identical cut perpendicular to the first one to form a cross-shaped opening. Transfer cucumber pieces cut side up to a large bowl. Sprinkle salt over the cucumbers, gently working some of the salt into the openings; let sit for 30 minutes. Rinse cucumbers and pat dry; set aside. In a medium bowl, vigorously stir together the remaining ingredients, except for the pine nuts, to make the filling. Working with 1 cucumber piece at a time, stuff about 2 tsp. of the filling into the opening. Press 3 or 4 pine nuts into the stuffing of each cucumber. Transfer to a platter and serve immediately, or allow cucumbers to ferment: nestle cucumber pieces, stuffed side up, in a plastic container; cover and let sit for 1 day at room temperature, then refrigerate until chilled. Cucumbers will continue to soften and will keep in the refrigerator for up to 1 week.