Testing - Simple thyme rack of lamb

I've never roasted a rack of lamb before, it looked so complicated. Now that we buy a half of a lamb at a time, part of what we get is the rack, so I've got to figure out how to prepare it. Looking into things, I realize it's a relatively quick thing. At first I was apprehensive about the Frenching of the rib bones, then suspected this may be unnecessary, and found my confirmation, thank to Google from two trusted sources : Serious Eats, and the Seattle Times. No Frenching for this cook, and more lamb!

The recipe below I think has all the basics, but is such a mish-mash of recipes that I didn't bother to save the sources. I'll likely be rewording things to my liking as I experiment with the techniques and the flavouring.

1 - Hmmm, I may not be posh enough to appreciate rack of lamb. I did not enjoy eating it. Perhaps I should have it in a restaurant to see if I may understand it better, then.

1 rack of lamb (about 2lbs) (Frenching optional)
15 to 20 fingerling potatoes
3 Tbsps olive oil
A few sprigs of thyme, leaved and minced.
Salt and pepper

1. Heat the oven to 425°F and arrange a rack in the bottom third. Meanwhile, let the lamb sit at room temperature.
2. Generously season the racks all over with salt and pepper. 
3. Heat 1 Tbsp of oil in a large frying pan over medium-high heat until shimmering. 
4. Place the lamb rack fat-side down in the pan and sear until golden brown, rotating the rack to brown as much of the fat as possible (you’re just trying to brown the fat, so don’t worry about flipping the rack over), about 3 to 4 minutes total. 
5. Transfer the rack to a rimmed baking sheet, fat side up with the bones facing the same direction. Sprinkle with half of the minced thyme.
6. Toss potatoes with 2 tablespoons of oil, and season with the remaining thyme, salt and pepper. Arrange potatoes around lamb.
7. Roast, rotating the pan halfway through the cooking time, until an instant-read thermometer inserted into the centre registers 125°F to 130°F for rare, about 25 to 35 minutes. Transfer the rack to a cutting board and let it rest uncovered for about 15 minutes.
8. Return potatoes to oven. Roast until tender, about 15 minutes more (the time it takes to let the rack rest)
9. Carve the rack into 4 (2-bone) chops and arrange them on a platter. (Some of the coating may fall off—just sprinkle it back on the lamb.) Season with salt and pepper and serve.