Cut the top (the part with the root) off the head of garlic and drizzle with olive oil. Roast in 400 degree F oven for 20-25 minutes. Cool enough to handle and remove cloves from papery outside.
In a food processor, blend roasted garlic cloves, sun dried tomatoes, egg yolks, lemon juice and salt. Use scraper to push ingredients back down into bowl and mix again.
With processor blending, slowly pour a small steady stream of oil and blend until thick and creamy.
To assemble the BLT:
Slice the ciabatta. Spread aioli liberally on bread. Layer with warm bacon, tomato and lettuce. Enjoy!
This makes two big sandwiches but you'll have leftover aioli. I actually used mine in place of mayo when making a tuna sandwich for the husband the next day.