In a small saucepan (or a small cup if you want to use the microwave), combine milk and 1 tablespoon honey and heat until it registers between 110 degrees F to 115 degrees F on an instant-read thermometer. Pour the mixture into bowl of an electric mixer and sprinkle over yeast. Let mixture stand for 10 minutes, until yeast is creamy.
Transfer bowl to mixer stand and attach paddle attachment. While mixing at low speed, gradually add eggs, all-purpose flour, sugar, and salt, and mix until blended. Gradually add all but 2 tablespoons of bread flour. Mix at medium speed until dough is smooth and elastic, about 5 minutes. Dough should not stick to sides of bowl; if it does, add some of all of remaining 2 tablespoons of bread flour until dough cleans sides of bowl. Add butter 1 tablespoon at a time, mixing at medium speed until it is blended into dough. (Dough will be very soft.) Transfer dough to a work surface and knead by hand a few times to ensure that butter is completely incorporated into dough. Shape dough into a ball and transfer it to a medium buttered bowl. Cover bowl with plastic wrap and set aside in a warm place for 1 1/2 to 2 hours, until it has doubled in volume.
Punch dough down to deflate it, and knead it a few times. Return dough to bowl, cover, and refrigerate for at least 4 hours (or up to 12 hours). Dough should have doubled in volume. If it hasn't, let it stand at room temperature until it has.
Butter bottom and sides of a 9" spring-form pan. Shape dough into a ball and arrange it, smooth side up, in center of pan. Flatten ball gently with your palm until it covers bottom of pan. Cover pan and let dough rise until it is puffed, about 1 hour. Position a rack in center of oven and preheat oven to 350 degrees F about 20 minutes before dough is ready.
In a small saucepan, heat remaining 1/3 cup honey just until warm. Brush honey over top of dough, then sprinkle with almonds. Bake cake for 30 to 35 minutes, until it is a lovely golden brown and a toothpick inserted into center of cake comes out clean. Cool cake in pan, set on a wire rack, for 15 minutes. Remove cake from pan and cool cake on the wire rack completely.