For the croutons: Heat the butter in a skillet over low heat. Add the garlic. When the butter just starts to bubble, add the bread cubes and toss to coat. Season with salt. Cook, tossing frequently, until the croutons are golden brown, about 10 minutes. Remove to a bowl, add the asiago and toss.
For the Caesar dressing: Add the mayo, anchovy paste, Dijon, Worcestershire, cayenne, lemon zest and juice, garlic and jalapeno to a food processor. Pulse together, then add the egg yolks and blend. With the machine running, slowly drizzle in the oil to ensure the dressing is emulsified. Add the asiago and blend again.
Feed the trimmed sprouts though the shredder with the slicer attachment of a food processor (or slice with a very sharp knife or a mandoline) and put into a large bowl. Pour over some of the dressing and toss to coat. Add more dressing to your liking. Put onto a platter and garnish with the croutons.