1. Sprinkle 1/3 cup sugar in a shallow, heavy 3½-qt. Dutch oven; cook over medium heat, stirring constantly, 3 minutes or until sugar is melted and syrup is light golden brown (sugar will clump). Remove from heat.
2. Stir together 1 Tbsp. flour and 2½ cups sugar in a large saucepan; add milk, and bring to a boil over medium-high heat, stirring constantly.
3. Gradually pour about one-fourth hot milk mixture into caramelized sugar, stirring constantly; gradually stir in remaining hot milk mixture until smooth. (Mixture will lump, but continue stirring until smooth.)
4. Cover and cook over low heat 2 minutes. Increase heat to medium; uncover and cook, without stirring, until a candy thermometer reaches 238° (soft-ball stage, about 10 minutes). Add butter, stirring until blended. Remove from heat and let stand, without stirring, until temperature drops to 110° (about 1 hour).
5. Pour into bowl of heavy-duty electric stand mixer. Add vanilla, and beat at medium speed (setting 4) with whisk attachment until spreading consistency (about 20 minutes).