Peel potatoes and cut into 1/4-inch cubes; put in a large bowl and cover with water.
In a 5- to 6-quart pan over medium heat, melt butter. Add shallots and garlic and stir until shallots are limp, about 1 minute.
Drain potatoes and add to pan, along with thyme and rosemary. Stir often until potatoes appear slightly translucent, about 8 minutes.
Add broth and stir often until potatoes are tender to bite and have absorbed most of the liquid, 12 to 15 minutes. Add cream and stir often until almost all is absorbed, 2 to 4 minutes. Add salt and pepper to taste.
Prepare through step 3 up to 2 hours ahead; cover and let stand at room temperature. Reheat and continue.