Question about ㅂ words changing into the -(으)ㄴ/는 것 form.
Here are some examples that confuse me. Why are they not all changing in the same way?

어렵다 어려운 것 What I perceive as the normal change.
돕다 돕는 것 Why is this one not becoming 도운 것? Also, following the correct rule of changing this way, why isn't it becoming 돕은 것?
굽다 굽는 것 Same confusion as above, and shows that the ㅗ is not the reason for the difference in change.
밉다 미운 것 Why is this one not becoming either 미운 것 nor 밉는 것?
맵다 매운 것 Shows that being a single-block word is not the explanation for this difference in change.

I got these answers from my workbook, so I know the changes are correct, but I don't know what extra rule my lesson didn't mention that explains these differences in changing.

Question

Question about ㅂ words changing into the -(으)ㄴ/는 것 form.
Here are some examples that confuse me. Why are they not all changing in the same way?

어렵다 > 어려운 것 > What I perceive as the normal change.
돕다 > 돕는 것 > Why is this one not becoming 도운 것? Also, following the correct rule of changing this way, why isn't it becoming 돕은 것? 
굽다 > 굽는 것 > Same confusion as above, and shows that the ㅗ is not the reason for the difference in change. 
밉다 > 미운 것 > Why is this one not becoming either 미운 것 nor 밉는 것?
맵다 > 매운 것 > Shows that being a single-block word is not the explanation for this difference in change.

I got these answers from my workbook, so I know the changes are correct, but I don't know what extra rule my lesson didn't mention that explains these differences in changing.

Answer

Your question is related with ㅂirregular verb/adjective and verbal adjective ending.
You must remember following three rules.

1. ㅂirregular verb/adjective rule is:
When a word stem with final consonant ㅂ + a particle start with vowel,
ㅂ changed 우 or 오.

* ㅂ => 오 (only with 아 vowel) => 와
돕다, 곱다.
돕(다) + 아요 => 도와요
곱(다) + 아요 => 고와요
돕(다) + 으면 => 도우면
곱(다) + 으면 => 고우면

* ㅂ => 우
어렵다, 쉽다, 덥다, 춥다, 귀엽다, 입다, 아름답다, 맵다, 눕다, 줍다.
덥(다) + 어요 => 더워요

NB. 입다, 잡다, 씹다, 좁다, 넓다, 뽑다, 접다 are not ㅂirregular verb/adjective

2. Verbal adjective ending for verb have four tesnses
* present            -는
저기 가는 자동차

* past              (으)ㄴ
어제 먹은 빵

* incomplete past    -던
어제 먹던 빵

* future             -(으)ㄹ
내일 먹을 밥

3. Verbal adjective ending for adjective have three tenses
* present   -(으)ㄴ
예쁜 꽃

* past      -던
예뻤던 꽃

* future  -(으)ㄹ
예쁠 꽃

Now analyze each words.
어려운 것 is composed with 어렵(다) + (으)ㄴ + 것
  어렵다 is ㅂirregular adjective.
  어려운 is present tense of verbal adjective ending of 어렵다

돕는 것 is composed with 돕(다) + 는 + 것
  돕다 is ㅂirregular verb.
  돕는 is present tense of verbal adjective ending of 돕다

cf)  
도운 것 is composed with 돕(다) + (으)ㄴ + 것
  돕다 is ㅂirregular verb.
  도운 is past tense of verbal adjective ending of 돕다

굽는 것 is composed with 굽(다) + 는 + 것
  굽다 is ㅂirregular verb.
  굽는 is present tense of verbal adjective ending of 굽다
  
미운 것 is composed with 밉(다) + (으)ㄴ + 것
  밉다 is ㅂirregular adjective.
  미운 is present tense of verbal adjective ending of 밉다

매운 것 is composed with 맵(다) + (으)ㄴ + 것
  맵다 is ㅂirregular adjective.
  매운 is present tense of verbal adjective ending of 맵다

Answer

it's a tough question to answer. I am not sure if there's any rules to explain. If there is, I believe some other Koreans would explain to you. In my opinion,  you just have to memorize each case. Sometimes you just speak that way. I know that English is also like that sometimes, right? But I could be wrong. If I am, please correct me.