Preheat the oven to 375 degrees F.
Brush some oil on the bread slices and arrange them on a sheet pan. Bake until golden brown, about 8 minutes. Remove the bread from the oven and set aside.
Melt 1 1/2 tablespoons of butter in a medium saucepan over medium heat. Whisk in the flour and cook, whisking, for 1 minute. Pour in 3/4 cup of the beer and simmer, whisking constantly, for 1 minute. Remove the saucepan from heat and add the cheeses, whisking until smooth.
In a large saute pan over medium heat, melt the remaining butter and add the fennel, leeks and chives. Saute until tender, and then stir in the remaining beer. Cook, stirring over medium heat, until all the onions are caramelized and the beer is mostly cooked off, about 15 to 20 minutes.
Spread the cheese fondue on the toasted bread. Put some of the fennel and leek mixture on top and arrange them on a serving platter. Sprinkle with fresh chives and serve.
A viewer or guest of the show, who may not be a professional cook, provided this recipe. It has not been tested for home use.