Coarsely chop hearts of romaine; shred radicchio; thinly slice endive lengthwise. Combine greens in a salad bowl.
Pour EVOO, four glugs, into a microwave safe dish. Add shallots to EVOO and place in microwave for 30 seconds on high. Remove from microwave and let stand 5 minutes. (On the stovetop, EVOO and shallots may be heated over low heat in a small pan for 2-3 minutes. Remove from heat and let stand until cool.) Pour EVOO and shallots in a bowl and whisk in 3 tablespoons balsamic vinegar. Drizzle vinaigrette over salad and toss to coat. Season with salt and pepper, to your taste.