The logic-only solution here is definitely a bit complex, but here's a quick stab at an explanation.
I'm starting off with the original screenshot, plus the two X's that Zenobia correctly pointed out could also be added (Clue 5: mac and cheese cannot be 350 degrees; Clue 11: 6 people cannot be 400 degrees.) It looks like the grid is then stuck at this point, but the way to break through is to compare clues 5 and 11 to each other:
mac and cheese --> 350 deg.
6 people --> 400 deg.
In my notations, --> means plus one increment (5 minutes) of baking time. (When a grid gets stuck and there are unfinished clues of the A >< B variety, I always write them all in the NOTES area so I can compare them and hopefully extract some useful data.)
Since 350 degress and 400 degrees cannot both have the same amount of baking time (as they're different options in the same category), and mac and cheese and 6 people are both 5 minutes less than the baking times of 350 deg. and 400 deg., that means mac and cheese and 6 people cannot have the same amount of baking time - and are therefore excludable from one another. This allows us to put an X into the yellow square.
That X then opens up 2 rows in the recipe/# of people subgrid where only the same two options are available (4 people and 6 people can only be baked ham and bean casserole, in some order). This allows us to X out any remaining open squares in those columns (baked ham and bean casserole) since we know they can only be 4 & 6. This allows us to put X's into the four blue squares.
Now (keeping in mind that the blue squares are X's), look at 350 degrees near the bottom of the grid. It can only be baked ham or candied yams. 2 people and 8 people cannot be either baken ham or candied yams - so they cannot be 350 degrees. This allows us to eliminate 350 degrees from 2 people and 8 people (X's in the pink squares), and that gives us a TRUE value for 4 people and 350 degrees. (forgot to color it in on the grid, sorry)
Now, since 4 people == 350 degrees, and 350 degrees cannot be 35 minutes, we can X out the light green square near the top right of the grid to indicate that 35 minutes CANNOT be 4 people. And that brings us back to clue #12 - if 35 minutes =/= 4 people, then 35 minutes must be mac and cheese. And from there the grid cascades to a complete solve.