In a large bowl, combine the water, yeast and honey and let stand for 5 minutes. Stir in 1 cup of the flour and 1/4 cup of the oil; let stand for 5 minutes. Stir in the remaining flour and the salt and knead until smooth. Transfer to an oiled bowl, cover with plastic and let stand for 1 hour.
Meanwhile, in a skillet, heat 1 tablespoon of the oil. Add the onion, cover and cook over moderate heat, stirring occasionally, for 10 minutes. Add the sugar, cover and cook, stirring occasionally, until browned, 10 minutes.
Preheat the oven to 450°. Oil a 9-by-13 inch rimmed baking sheet. Transfer the dough to the sheet and press it down to fit. Dimple the dough all over with your fingers and drizzle with 2 tablespoons of the olive oil. Let the dough rise until puffed, about 20 minutes.
Scatter the onions over the dough. Arrange the pear over the onions and sprinkle with the blue cheese. Drizzle the remaining 2 tablespoons of oil over the focaccia and bake for 20 minutes, until golden. Transfer to a rack to cool. Serve.