Dissolve the yeast in the warm water; stir in ½ teaspoon of the honey and set aside for 10 minutes.
Mix the remaining 2½ teaspoons honey with the salt, olive oil, and cool water and set aside.
Put the flour in the bowl of a food processor. With the processor running, slowly pour the honey-oil mixture in through the feed tube. Then pour in the dissolved yeast. Process until the dough forms a ball on the blade. If it is too sticky, sprinkle on a little more flour.
Scrape the dough out onto a lightly floured surface and knead until smooth.
Transfer to an oiled bowl and let rest, covered, for 30 minutes.
Divide the dough into 4 equal parts.
Roll each into a smooth, tight ball. Put on a flat sheet or dish, cover with a damp towel and refrigerate for 1 to 3 hours.
One hour before baking, remove the dough from the refrigerator and let it come to room temperature before rolling and shaping.
Preheat the oven, preferably with a pizza stone inside, to 500 degrees for 30 minutes while getting the pizza ready.
Cut the salmon into 2-inch squares and reserve.
Roll or stretch each ball of dough into four 9-inch circles. Put the circles on an oiled, floured baking sheet.
Brush each pizza with olive oil to within one inch of the edge and sprinkle with red onion.
Put the pizzas in the oven and bake 8 to 12 minutes, until the crusts are golden brown.
While the pizzas are baking, mix the dill with the crème fraîche or sour cream and season with pepper.
When the pizzas are done, transfer to warm dinner plates and spread with the crème fraiche or sour cream mixture.
Arrange the pieces of salmon on top and, if desired, put a tablespoon of golden caviar in the center of each and spoon a little black caviar on the golden caviar.
Garnish each pizza with a sprig of dill and serve.