Just a basic fingerless mitt knitted in a K3, P1 rib with a 40-stitch cast on.

Here’s the basic pattern:
C/O 40 stitches, using a stretchy cast on (I used German twisted cast on)
establish pattern: K3, P1 across
continue in pattern until wrist cuff is 3 inches long (24 rounds) or desired length

Begin the thumb gusset increases:
K3, P1 x 5, K3, PM, M1L, K1, M1R, PM, (K3, P1] x 4

K 2 rounds in pattern, knitting all the gusset stitches

Continue working in pattern, doing the gusset increases after the first marker and before the last marker, knitting the stitches in between every fourth round, until there are 15 stitches between the markers.

Knit 2 more rounds in pattern

Next round: K3, P1 x 5, K3, put 15 thumb gusset stitches on a holder, cast on one stitch using backward loop cast on, K3, P1 x 4

Continue working in K3, P1 pattern until the mitt is the length you like. I worked 20 rounds.

Cast off. I used the sewn cast off.

Move the 15 thumb gusset stitches from the holder to the needle(s) and pick up and knit 4 stitches to close the gap

Rnd 1 of thumb: K16, k2tog, k1
knit 8 more rounds, then cast off (I use sewn cast off).