Mash garlic and salt in medium metal bowl with pestle or back of spoon until paste forms. Whisk in egg yolks, 3 tablespoons water, lemon juice, and mustard. Set bowl over saucepan of barely simmering water (do not allow bottom of bowl to touch water) and whisk constantly until mixture thickens and instant-read thermometer inserted into mixture registers 140°F for 3 minutes, 6 to 7 minutes total. Remove bowl from over water. Cool mixture to room temperature, whisking occasionally, about 15 minutes.

Gradually whisk 1 cup oil into yolk mixture in very thin slow stream, whisking until sauce is thick. Season with pepper and more salt, if desired. Cover and chill.

Cut slit lengthwise down side of each pepper. Cut cheese into small rectangular pieces to fit inside peppers. Insert 1 piece cheese into each pepper; press to enclose. do ahead Sauce and peppers can be made 1 day ahead. Cover separately and chill.

Heat 1 tablespoon oil in heavy large nonstick skillet over medium-high heat. Add peppers to skillet; cook until browned in spots and cheese melts (some cheese may ooze out of peppers), turning occasionally, 1 to 2 minutes. Arrange peppers on platter. Serve with sauce for dipping.