I've played about 75 sessions of 5E with characters in Tier 3 and Tier 4. DMs complain about how high CR monsters don't hit hard enough (which is facts) but it's also true that low CR monsters don't go down fast enough. For example, you would think that a CR2 ogre would go down quickly to a high level martial. Probably not. They have 59 hit points. Yes, they might drop in one round to a smiting paladin or a fighter using action surge. But most other classes will spend 2 turns grinding down that ogre. And do the fighter and paladin actually want to use their limited resources on a monster that might not even be able to hit them? Probably not. And yet what's the point of being a high level martial if you can't wreck a clan of ogres single handedly?
This is a long way of saying I think there are two ways to build "minions", and I think both should be used.
Challenging high level players means that "minions" need to have fewer hit points, but more damage output and higher to hit bonuses. Here's how I do that...
Attack bonuses are +3 per tier of the player, at minimum. This is a simple formula I can keep in my head. For 11th level characters, I would increase the attack bonus of the ogre to +9.
For damage, I take the static damage and 1) keep it the same, or 2) multiply it by the tier of the player. Using the ogre as an example, their great club does 13 damage. So I would either keep the damage at 13 or increase it to 39, depending upon what I need to build an appropriate encounter.
For hit points, I either 1) keep the same, or 2) divide by the tier of the player. This ogre would either have 59 hit points or 20 hit points.
Putting it all together, I can use this formula to build two different types of ogre "minions".
The first would have +9 to hit, do 13 damage, and have 20 hit points. This is a true minion--cannon fodder. You could throw 5 to 10 of these at a Tier 4 martial.
The second would have +9 to hit, do 39 damage, and have 59 hit points. This is an upleveled ogre. They are a meaningful threat to a Tier 4 martial but will go down in 1 or 2 rounds. Two or three of these can challenge a Tier 4 martial for a short period of time.
Hope this is a useful contribution to the conversation.