In a small saucepan, heat 6 tablespoons of milk and 2 tablespoons water until just slightly warm. Pour into a bowl with 1 heaping teaspoon of sugar, whisk to dissolve. Add 1/4 ounce of fresh yeast and whisk to break up and dissolve the yeast. Pour into a standing mixer bowl with the paddle attachment. Turn on low, add 5 tablespoons melted butter. Add the flour and salt and mix just until it comes together. Raise the speed to medium, add the eggs, one at a time, and mix until it becomes elastic and smooth. Turn dough into a bowl, cover with a damp tea towel, and let it rest and proof for 10 minutes. Punch down and allow to rise another 5 minutes. The dough should not proof too long, or the savarins will become crumbly.
Preheat oven to 400 degrees F.
Butter each savarin ring. Using your finger, schmear baba dough in the ring to fill it up half way, using about 1 ounce of dough. It will stick to your fingers, but don't dip your fingers in flour to prevent this. Let the dough rise until it reaches the top of the ring, about 30 minutes. Bake the savarins for 15 minutes. Let the cool in their rings then turn them out.
To prepare the syrup, place all the ingredients in a saucepan and bring to a boil. Dip the savarins in the syrup then place them in a rectangular pan and drizzle more syrup over them. Cover and let them soak overnight. Add more syrup the next day if they'll absorb it.
To serve, cut up the strawberries and stir the honey into the creme fraiche. Serve the savarin on a plate with a spoonful of strawberries and a large dollop of honey-creme fraiche. You may put the leftover syrup in a decorative bottle and pour more of it over the dessert as you serve it at the table.