I'm planning a cycle tour from Bormio (Italy) to Annecy (France), estimating about 80km / day. Has anybody done this? Any recommendation for routes, preferably taking in cols / passes along the way.
The most direct route between Bormio and Annecy goes through Switzerland, which has a network of national bike routes which consists mostly of well maintained side roads. One option is to cross the border to St. Moritz, take a combination of these routes to Geneve and ride to Annecy from there (take the shortcut route over Mt. Saléve instead of flatter one). I rode the route 4 some years ago and I strongly recommend it. There is a Swiss cycle route map that shows a list of recommended climbs and shortcuts, which is great for changing the route on the fly.
One caveat is that Switzerland is an expensive country and staying on Italian side of the border might save significant money. Border crossings inside Schengen area are more or less a non-issue.
Regardless of whether my suggestion below is of any use to you: As you're looking for cols you might want to look into some of the resources from the club de cent cols, some of which are available to non-members. Their Randonnées Permanentes might also be of interest to guide some of your route planning (especially the "Cent cols en Savoie Mont Blanc" route for the western end, but there are routes in Switzerland and Italy as well).
I've been looking into day rides not far south of Annecy recently, so have spent some time with (mainly offline) maps of the French side. There aren't that many border crossings assuming you want to avoid main roads (which I assume you do). If you didn't want to pass through a third country, crossing from Pré-Saint-Didier to Bourg-Saint-Maurice looks good,for example, as it avoids going too far south/too near Torino. The border itself is the Col du Petit St. Bernard, and at a quick look you could reach the Italian side on smaller roads that run parallel to the main roads.
I suggest to avoid Switserland, except for a small corner, because it is horribly expensive and boring. Stick as long as possible to Italy, my favorite biking country. I also suggest to do a couple of legendary passes that you could skip if you followed the line of least action, but that will give you lasting memories of the riding Italy's backcountry.
Here is my recommended route, all done myself, but not in one season: Bormio - Grosio - Passo di Mortirolo - Edolo - Passo Aprica - Morbegno - Passo San Marco - Lenna - Passo San Pietro - Lecce - Como - Biella - Aosta - Col Grand Saint Bernard - Martigny - Col du Forclaz - Chamonix - Col des Aravis - Annecy. All in all 700 km and 14000 meter elevation gain.
That sounds awesome fun.
I'd suggest looking at Strava's heatmap and see where people ride - a road good for cars might not be good for bikes.
Your language might come into it too - whether you're more comfortable in Switzerland or Italy.
Your minimum is one border crossing from France to Italy, or two from France to Switzerland to Italy, or you may hop back and forth.
Germany is probably too far out of your way, but Liechtenstein and western Austria are within reach.
Which passes to take? I can't answer that.