Spread each flatbread with some of the hummus, then top with the caramelized onions, olives, and anchovies. Garnish with fresh thyme leaves. Cut into wedges and serve.
In an electric mixer fitted with the paddle attachment, combine the yeast, sugar, and water. Mix for 1 minute on low speed and let stand until the mixture just begins to bubble. Attach the dough hook and add both flours and the salt to the yeast mixture. Mix until it forms a mass; the dough should be sticky. Continue to add additional flour, if necessary, until the surface is dry enough to handle and dry enough to roll.
Divide the dough into 4 pieces, roll into balls, and lightly brush with oil. Place on a floured surface and cover the balls with plastic wrap and a clean cloth and let proof for 2 hours at room temperature; or, place on a lightly greased baking sheet, cover, and let proof overnight in a refrigerator.
Preheat a grill or preheat the oven to 425 degrees F.
To form flatbread, pat each piece of dough out into a 5-inch disk and sprinkle liberally with flour. Roll each disk, on a floured surface, into a 10-inch diameter circle. Puncture the dough liberally with a fork to keep it from rising. Grill or bake each on a pizza stone or a lightly greased sheet pan for about 5 minutes or until dough starts to get crisp on the edges but still remains chewy.
Place beans, garlic, harissa, lemon juice, and tahini in the bowl of a food processor and process until smooth. With the machine running, slowly add the olive oil until emulsified. Season with salt and pepper, to taste.
Heat oil and butter in a large pan over medium heat. Add the onions and sugar and cook slowly until deep golden brown, stirring occasionally. Remove from the heat and stir in the thyme.