Allow egg yolks to reach room temperature.
Combine salt, mustard, paprika, and pepper in a small mixing bowl. Add yolks; beat at medium-high speed of an electric mixer 1 to 2 minutes or until thickened. Add vinegar; beat an additional 30 seconds.
Add 1/4 cup oil, one drop at a time, to yolk mixture, beating constantly at medium-high speed of an electric mixer. Be sure that oil is thoroughly combined in egg yolk mixture before adding another drop.
Add 1 1/4 cups oil, 1 tablespoon at a time, being sure oil is thoroughly combined in yolk mixture before adding another tablespoon. Scrape mixing bowl frequently during entire procedure. Add remaining 1/2 cup oil alternately with lemon juice and water, beating constantly.
Spoon mixture into a serving bowl. Add garlic. Cover and refrigerate overnight. Remove garlic slices and discard. Stir mixture before serving.