CARAMELIZE THE ONIONS:
Add 2-3 Tbsp butter to a large skillet and heat over MED to MED-HIGH heat. Add diced onions to pan, and saute, stirring often, for 3-5 minutes.
Season with thyme, salt, and pepper.
Reduce heat to MED-LOW and saute, stirring occasionally, for 10-20 minutes, until onions are soft and golden brown in color.
Remove from heat and set aside.
COOK THE POTATOES:
If using baby yukon gold potatoes, halve the smaller ones, and quarter the larger ones.
Add sliced potatoes to a large clean, dry pot. Cover with cold water, about 1" above the potatoes, and season with 1 tsp salt.
Cover, and bring to a boil. Once boiling, remove lid and boil for 15-20 minutes, or until potatoes are tender when pierced with a fork.
Drain potatoes, then return to the same pot.
Microwave heavy cream and butter for 1 minute, then pour over cooked potatoes.
Mash until desired consistency. Alternatively, beat with a hand mixer.
Use a wooden spoon to stir in salt, pepper, dijon mustard, horseradish and caramelized onions.
Garnish with minced parsley.